{"presentation":{"slides":[{"elements":[{"x":0,"y":0,"width":99.782135076253,"height":100,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5dea6ff5a8e67.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":994,"height":515,"originalImage":{"path":"images\/file-5dea6f93e512a.jpg#tmp","mime":"image\/jpeg","height":4000,"width":6000}},"alt":"A desktop computer, a laptop and other technology"},"subContentId":"6d6c6c88-37ce-4968-a3eb-01ca537088eb","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":0,"y":19.495661605206074,"width":78.9010989010989,"height":73.31887201735357,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Matrix Properties<\/h2>\n\n

Learning Outcome(s)<\/h3>\n\n
By the end of this module, you should be able to:<\/p>\n\n
\n\t
Compute the product of two matrices and identify whether the product is well-defined or not.<\/li>\n\t
Define symmetric and skew-symmetric matrix and determine whether a given matrix is symmetric or skew-symmetric or neither.<\/li>\n\t
Use column\/row method to multiply two matrices.<\/li>\n\t
Connect inverse matrices with number of solutions to a given linear system.<\/li>\n<\/ul>\n"},"subContentId":"50b41976-55b0-4052-9b62-d1661ecdc4af","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":80,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":0,"y":0,"width":99.782135076253,"height":99.569892473118,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"rgb(255, 255, 255)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"2f20f6c0-ff09-46b2-bf3a-fd6c6d6111fe","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":9.878087912087913,"y":19.495661605206074,"width":81.0989010989011,"height":73.31887201735357,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"
Overview<\/h3>\n\n
In this module, we will learn how to multiply two matrices using dot products, and column\/row methods<\/p>\n\n
We'll also learn about symmetric and skew symmetric matrices.<\/p>\n\n
When \\[ A = A^{T},\\] we say that A is symmetric; when \\[ A = -A^{T},\\] we say that A is skew-symmetric.<\/p>\n"},"subContentId":"30011ec9-d0a7-4d7e-a204-5280b243cc57","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":42.483660130719,"y":0,"width":57.298474945534,"height":99.569892473118,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"rgb(0, 0, 0)","borderWidth":"0","borderStyle":"solid","borderColor":"#000","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"d37d7a8a-e04e-4ebb-b945-60322c6d4be7","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":0,"y":-0.42338709677419,"width":42.265795206972,"height":100,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"rgb(255, 255, 255)","borderWidth":"0","borderStyle":"solid","borderColor":"rgb(255, 255, 255)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"2a838250-a3fb-408a-9041-993143c55203","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":43.956043956043956,"y":13.015184381778742,"width":54.030501089325,"height":60.033627450980816,"action":{"library":"H5P.Video 1.6","params":{"visuals":{"fit":true,"controls":true},"playback":{"autoplay":false,"loop":false},"l10n":{"name":"Video","loading":"Video player loading...","noPlayers":"Found no video players that supports the given video format.","noSources":"Video is missing sources.","aborted":"Media playback has been aborted.","networkFailure":"Network failure.","cannotDecode":"Unable to decode media.","formatNotSupported":"Video format not supported.","mediaEncrypted":"Media encrypted.","unknownError":"Unknown error.","invalidYtId":"Invalid YouTube ID.","unknownYtId":"Unable to find video with the given YouTube ID.","restrictedYt":"The owner of this video does not allow it to be embedded."},"sources":[{"path":"https:\/\/www.youtube.com\/watch?v=2spTnAiQg4M","mime":"video\/YouTube","copyright":{"license":"U"}}]},"subContentId":"23e0266d-2105-4d30-9940-f8b8a0575ba2","metadata":{"contentType":"Video","license":"U","title":"Multiply two matrices"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":1.098901098901099,"y":4.338394793926247,"width":40.087145969499,"height":92.043010752688,"action":{"library":"H5P.ExportableTextArea 1.3","params":{"exportNotSupported":"Export not supported on your device","exportComments":false,"index":0,"label":"
Watch the video.<\/strong><\/p>\n\n
What is the dimension of the first matrix in the product?<\/strong><\/p>\n\n
What is the dimension of the second matrix in the product?<\/strong><\/p>\n\n
What is a general rule in order for a matrix product to be well-defined? <\/p>\n\n
Type your answer below.<\/strong><\/p>\n"},"subContentId":"b463bbf5-a168-423a-be95-86cc0ee9972b","metadata":{"contentType":"Exportable Text Area","license":"U","title":"Untitled Exportable Text Area"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":0,"y":0,"width":54.248366013072,"height":99.569892473118,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"rgb(0, 0, 0)","borderWidth":"0","borderStyle":"solid","borderColor":"#000","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"a882295d-e770-41cd-b44b-6edc65ab1fad","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":54.466230936819,"y":0,"width":45.315904139434,"height":99.569892473118,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"rgb(255, 255, 255)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"083cc0bd-aa69-4208-829e-8689a0d5cc80","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":1.098901098901099,"y":13.015184381778742,"width":52.069716775599,"height":57.854987745097894,"action":{"library":"H5P.Video 1.6","params":{"visuals":{"fit":true,"controls":true},"playback":{"autoplay":false,"loop":false},"l10n":{"name":"Video","loading":"Video player loading...","noPlayers":"Found no video players that supports the given video format.","noSources":"Video is missing sources.","aborted":"Media playback has been aborted.","networkFailure":"Network failure.","cannotDecode":"Unable to decode media.","formatNotSupported":"Video format not supported.","mediaEncrypted":"Media encrypted.","unknownError":"Unknown error.","invalidYtId":"Invalid YouTube ID.","unknownYtId":"Unable to find video with the given YouTube ID.","restrictedYt":"The owner of this video does not allow it to be embedded."},"sources":[{"path":"https:\/\/www.youtube.com\/watch?v=7CBkZq3eQ_0","mime":"video\/YouTube","copyright":{"license":"U"}}]},"subContentId":"42812c63-6965-4a3a-b463-7ea421bcad5f","metadata":{"contentType":"Video","license":"U","title":"Matrix-vector Multiplication"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":57.142857142857146,"y":4.338394793926247,"width":41.176470588235,"height":92.043010752688,"action":{"library":"H5P.ExportableTextArea 1.3","params":{"exportNotSupported":"Export not supported on your device","exportComments":false,"index":0,"label":"
Watch the video.<\/strong><\/p>\n\n
When we use column interpretation to find the product of a matrix and a column vector, what kind of product was used in the video? <\/strong><\/p>\n\n
Type your answer below.<\/strong><\/p>\n"},"subContentId":"13607bfb-a964-4a8a-9423-0e613880c875","metadata":{"contentType":"Exportable Text Area","license":"U","title":"Untitled Exportable Text Area"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":49.019607843137,"y":0,"width":50.762527233115,"height":100,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"rgb(255, 255, 255)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"083cc0bd-aa69-4208-829e-8689a0d5cc80","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":0,"y":0,"width":49.673202614379,"height":99.569892473118,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"rgb(0, 0, 0)","borderWidth":"0","borderStyle":"solid","borderColor":"#000","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"d18c8b79-044e-42d5-a57e-daf421e54ef8","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":54.94505494505495,"y":13.015184381778742,"width":41.176470588235,"height":74.838709677419,"action":{"library":"H5P.ExportableTextArea 1.3","params":{"exportNotSupported":"Export not supported on your device","exportComments":false,"index":0,"label":"
Read the handout<\/a> about matrix. <\/strong><\/p>\n\n
What's the answer to Question 1 on the last page?<\/strong><\/p>\n\n
Type your answer and expain it below.<\/strong><\/p>\n"},"subContentId":"13607bfb-a964-4a8a-9423-0e613880c875","metadata":{"contentType":"Exportable Text Area","license":"U","title":"Untitled Exportable Text Area"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":6.576241758241759,"y":4.324837310195228,"width":38.24175824175824,"height":42.950108459869845,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5edaaff43339f.png","mime":"image\/png","copyright":{"license":"U"},"width":1744,"height":858},"alt":"Screenshot of the handout last page"},"subContentId":"6faeff38-1a7b-4a2d-83c4-3ca14a67d2a5","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":4.3572984749455,"y":4.3010752688172,"width":40,"height":40,"action":{"library":"H5P.Link 1.3","params":{"linkWidget":{"protocol":"http:\/\/","url":"wiki.ubc.ca\/images\/1\/19\/SECTIONS_Framework.pdf"},"title":"SECTIONS"},"subContentId":"787393eb-21cd-4bff-95a2-f80d8fa1e6f2","metadata":{"contentType":"Link","license":"U"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":true,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":49.019607843137,"y":0,"width":50.762527233115,"height":100,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"rgb(255, 255, 255)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"083cc0bd-aa69-4208-829e-8689a0d5cc80","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":54.466230936819,"y":12.903225806452,"width":41.176470588235,"height":74.838709677419,"action":{"library":"H5P.ExportableTextArea 1.3","params":{"exportNotSupported":"Export not supported on your device","exportComments":false,"index":0,"label":"
Watch the video.<\/p>\n\n
Can you find the eigenvalues of matrix S?<\/strong><\/p>\n\n
What about A?<\/strong><\/p>\n\n
Type your answer below.<\/strong><\/p>\n"},"subContentId":"13607bfb-a964-4a8a-9423-0e613880c875","metadata":{"contentType":"Exportable Text Area","license":"U","title":"Untitled Exportable Text Area"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":1.0963252747252747,"y":8.65646420824295,"width":45.934065934065934,"height":60.30368763557483,"action":{"library":"H5P.Video 1.6","params":{"visuals":{"fit":true,"controls":true},"playback":{"autoplay":false,"loop":false},"l10n":{"name":"Video","loading":"Video player loading...","noPlayers":"Found no video players that supports the given video format.","noSources":"Video is missing sources.","aborted":"Media playback has been aborted.","networkFailure":"Network failure.","cannotDecode":"Unable to decode media.","formatNotSupported":"Video format not supported.","mediaEncrypted":"Media encrypted.","unknownError":"Unknown error.","invalidYtId":"Invalid YouTube ID.","unknownYtId":"Unable to find video with the given YouTube ID.","restrictedYt":"The owner of this video does not allow it to be embedded."},"sources":[{"path":"https:\/\/www.youtube.com\/watch?v=ZTNniGvY5IQ","mime":"video\/YouTube","copyright":{"license":"U"}}]},"subContentId":"443a0805-05e5-4da1-89b8-e2ee5a0c987e","metadata":{"contentType":"Video","license":"U","title":"Symmetric Matrix"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":23.038241758241757,"y":29.616268980477223,"width":61.53846153846154,"height":51.62689804772234,"action":{"library":"H5P.TrueFalse 1.8","params":{"media":{"disableImageZooming":false},"correct":"false","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false},"l10n":{"trueText":"True","falseText":"False","score":"You got @score of @total points","checkAnswer":"Check","showSolutionButton":"Show solution","tryAgain":"Retry","wrongAnswerMessage":"Wrong answer","correctAnswerMessage":"Correct answer","scoreBarLabel":"You got :num out of :total points"},"confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"question":"
True or False?<\/p>\n\n
There are square matrices A and B so that AB is invertible but neither A nor B is invertible. <\/p>\n"},"subContentId":"67d80075-bba1-47a7-842c-75a1b2f7e831","metadata":{"contentType":"True\/False Question","license":"U","title":"True\/False Question"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":"
check page 5 on the handout. <\/p>\n"}],"slideBackgroundSelector":{}},{"slideBackgroundSelector":{},"elements":[{"x":3.2679738562092,"y":6.4381720430108,"width":93.464052287582,"height":85.591397849462,"action":{"library":"H5P.ExportableTextArea 1.3","params":{"exportNotSupported":"Export not supported on your device","exportComments":false,"index":0,"label":"
After watching the given videos and reading the handout, can you summerize the concepts that are included in this module?<\/p>\n\n
<\/p>\n"},"subContentId":"0eeeb22a-dc4b-47dd-939a-85de43fb5c77","metadata":{"contentType":"Exportable Text Area","license":"U","title":"Untitled Exportable Text Area"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}]},{"elements":[{"x":0,"y":0,"width":99.782135076253,"height":99.569892473118,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"rgb(255, 255, 255)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"2f20f6c0-ff09-46b2-bf3a-fd6c6d6111fe","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":2.1786492374728,"y":2.1505376344086,"width":97.60348583878,"height":97.41935483871,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"
Successful completion of module 3 comprises the following:<\/h2>\n\n
I have...<\/p>\n\n
\n\t
<\/em> watched the videos about how to multiply two matrices<\/li>\n\t
<\/em> learned three ways to multiply two matrices<\/li>\n\t
<\/em> tried all the polling questions on Quercus <\/li>\n\t
posted at least one post on Piazza forum <\/li>\n\t
read the handout and attempted all the questions in the handout <\/li>\n\t
submitted homework assignment 3<\/li>\n<\/ul>\n"},"subContentId":"253e7956-3a69-46b8-95e3-8884a03cccc9","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":0,"y":0,"width":99.782135076253,"height":99.569892473118,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"rgb(255, 255, 255)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"2f20f6c0-ff09-46b2-bf3a-fd6c6d6111fe","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":2.1786492374728,"y":2.1505376344086,"width":97.60348583878,"height":97.41935483871,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"
On the next page, click on Export Text. Save this as a doc, docx, or PDF file and submit this through the assignment submission link on Blackboard.<\/strong><\/h2>\n"},"subContentId":"253e7956-3a69-46b8-95e3-8884a03cccc9","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}}],"keywordListEnabled":true,"globalBackgroundSelector":{"fillGlobalBackground":"#ffffff"},"keywordListAlwaysShow":false,"keywordListAutoHide":true,"keywordListOpacity":90},"override":{"activeSurface":false,"hideSummarySlide":true,"summarySlideSolutionButton":true,"summarySlideRetryButton":true,"enablePrintButton":true,"social":{"showFacebookShare":false,"facebookShare":{"url":"@currentpageurl","quote":"I scored @score out of @maxScore on a task at @currentpageurl."},"showTwitterShare":false,"twitterShare":{"statement":"I scored @score out of @maxScore on a task at @currentpageurl.","url":"@currentpageurl","hashtags":"h5p, course"},"showGoogleShare":false,"googleShareUrl":"@currentpageurl"},"showSolutionButton":"off","retryButton":"off"},"l10n":{"slide":"Slide","score":"Score","yourScore":"Your Score","maxScore":"Max Score","total":"Total","totalScore":"Total Score","showSolutions":"Show solutions","retry":"Retry","exportAnswers":"Export text","hideKeywords":"Hide sidebar navigation menu","showKeywords":"Show sidebar navigation menu","fullscreen":"Fullscreen","exitFullscreen":"Exit fullscreen","prevSlide":"Previous slide","nextSlide":"Next slide","currentSlide":"Current slide","lastSlide":"Last slide","solutionModeTitle":"Exit solution mode","solutionModeText":"Solution Mode","summaryMultipleTaskText":"Multiple tasks","scoreMessage":"You achieved:","shareFacebook":"Share on Facebook","shareTwitter":"Share on Twitter","shareGoogle":"Share on Google+","summary":"Summary","solutionsButtonTitle":"Show comments","printTitle":"Print","printIngress":"How would you like to print this presentation?","printAllSlides":"Print all slides","printCurrentSlide":"Print current slide","noTitle":"No title","accessibilitySlideNavigationExplanation":"Use left and right arrow to change slide in that direction whenever canvas is selected.","accessibilityCanvasLabel":"Presentation canvas. Use left and right arrow to move between slides.","containsNotCompleted":"@slideName contains not completed interaction","containsCompleted":"@slideName contains completed interaction","slideCount":"Slide @index of @total","containsOnlyCorrect":"@slideName only has correct answers","containsIncorrectAnswers":"@slideName has incorrect answers","shareResult":"Share Result","accessibilityTotalScore":"You got @score of @maxScore points in total","accessibilityEnteredFullscreen":"Entered fullscreen","accessibilityExitedFullscreen":"Exited fullscreen"}}

Matrix Product

Xinli Wang