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Answer:<\/strong> False<\/div>\n\n
Reasoning:<\/strong> In general, the range of a linear map is a subspace of its codomain. In particular, in this case, \\( \\text{Range}(L)\\subseteq M_{3\\times4}(\\mathbb{R}) \\), so \\( \\text{Range}(L) \\) is not contained in \\( \\mathbb{R}^2 \\).<\/div>\n","tip":"","notChosenFeedback":""},"text":"
True<\/div>\n"},{"correct":true,"tipsAndFeedback":{"chosenFeedback":"
Answer:<\/strong> False<\/div>\n\n
Reasoning:<\/strong> In general, the range of a linear map is a subspace of its codomain. In particular, in this case, \\( \\text{Range}(L)\\subseteq M_{3\\times4}(\\mathbb{R}) \\), so \\( \\text{Range}(L) \\) is not contained in \\( \\mathbb{R}^2 \\).<\/div>\n","tip":"","notChosenFeedback":""},"text":"
False<\/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":"
Let \\( L\\colon\\mathbb{R}^2\\to M_{3\\times4}(\\mathbb{R}) \\) be a linear map.<\/p>\n\n
True or False: \\( \\text{Range}(L) \\) is a subspace of \\( \\mathbb{R}^2 \\).<\/p>\n"}