{"media":{"disableImageZooming":false},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\\(1\\)<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\\(\\sqrt{2}\\)<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"

Answer:<\/strong> 2<\/div>\n\n
Reasoning:<\/strong> By definition, \\[ \\|I\\|^2 = \\langle I, I \\rangle = \\text{trace}(I^TI) = \\text{trace}(I) = 2. \\]<\/div>\n","notChosenFeedback":"
Answer:<\/strong> 2<\/div>\n\n
Reasoning:<\/strong> By definition, \\[ \\|I\\|^2 = \\langle I, I \\rangle = \\text{trace}(I^TI) = \\text{trace}(I) = 2. \\]<\/div>\n"},"text":"
\\(2\\)<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
\\(\\sqrt{3}\\)<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":true,"enableSolutionsButton":false,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":false,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"Check","submitAnswerButton":"Submit","showSolutionButton":"Show solution","tryAgainButton":"Retry","tipsLabel":"Show tip","scoreBarLabel":"You got :num out of :total points","tipAvailable":"Tip available","feedbackAvailable":"Feedback available","readFeedback":"Read feedback","wrongAnswer":"Wrong answer","correctAnswer":"Correct answer","shouldCheck":"Should have been checked","shouldNotCheck":"Should not have been checked","noInput":"Please answer before viewing the solution","a11yCheck":"Check the answers. The responses will be marked as correct, incorrect, or unanswered.","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again."},"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":"
Consider \\( M_{2\\times2}(\\mathbb{R}) \\) with inner product defined by \\[ \\langle A, B \\rangle = \\text{trace}(B^T A). \\] Let \\( \\|\\cdot\\| \\) be the norm induced by \\( \\langle\\,,\\rangle \\). Determine \\( \\|I\\|^2 \\), where \\( I \\) is the \\( 2\\times2 \\) identity matrix.<\/p>\n"}