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a. <\/strong>\\( 0 \\)<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
b.<\/strong> \\( \\sqrt{3} \\)<\/div>\n"},{"correct":true,"tipsAndFeedback":{"chosenFeedback":"
Answer: <\/strong>The only correct choice is option c.<\/div>\n\n
Reasoning<\/strong>: The singular values of \\( A \\) are the non-negative square roots of the eigenvalues of \\( A^T A \\). Thee eigenvalues of \\( A^TA \\) are computed to be \\( 5 \\) and \\( 6 \\). So the singular values of \\( A \\) are \\( \\sqrt 5 \\) and \\( \\sqrt 6 \\).<\/div>\n","notChosenFeedback":"
Answer: <\/strong>The only correct choice is option c.<\/div>\n\n
Reasoning<\/strong>: The singular values of \\( A \\) are the non-negative square roots of the eigenvalues of \\( A^T A \\). Thee eigenvalues of \\( A^TA \\) are computed to be \\( 5 \\) and \\( 6 \\). So the singular values of \\( A \\) are \\( \\sqrt 5 \\) and \\( \\sqrt 6 \\).<\/div>\n","tip":""},"text":"
c. <\/strong>\\( \\sqrt{5} \\)<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
d.<\/strong> \\( \\sqrt{7} \\)<\/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":"
Which of the following are singular values of \\( A= \\begin{bmatrix} 1&2\\\\-2&1\\\\0&1 \\end{bmatrix} \\)? Select all that are.<\/p>\n"}