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Let \\( L\\colon\\mathbb{R}^2\\to M_{2\\times3}(\\mathbb{R}) \\) be a linear map, let \\( \\mathcal{B} \\) and \\( \\mathcal{C} \\) be bases for \\( \\mathbb{R}^2 \\) and \\( M_{2\\times3}(\\mathbb{R}) \\), respectively.<\/p>\n\n

Let \\( {}_\\mathcal{C}[L]_\\mathcal{B} \\) be the matrix of \\( L \\) with respect to the bases \\( \\mathcal{B} \\) and \\( \\mathcal{C} \\).<\/p>\n\n

How many rows does \\( {}_\\mathcal{C}[L]_\\mathcal{B} \\) have?<\/p>\n"},"library":"H5P.AdvancedText 1.1","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"1ce2d410-a1b6-46ae-9ecb-811164f76753"},"useSeparator":"auto"},{"content":{"params":{"panels":[{"content":{"params":{"text":"

Answer:<\/strong> 6<\/p>\n\n

Reasoning:<\/strong> The matrix \\( {}_C[L]_\\mathcal{B} \\) will have size \\( 6\\times2 \\) (because \\( \\dim(M_{2\\times3}(\\mathbb{R})=6 \\) and \\( \\dim(\\mathbb{R}^2)=2 \\)), so it will have 6 rows.<\/p>\n"},"library":"H5P.AdvancedText 1.1","subContentId":"4b963165-47bc-4c9f-9c3d-b68395b3341e","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"title":"Click to see the solution"}],"hTag":"h4"},"library":"H5P.Accordion 1.0","metadata":{"contentType":"Accordion","license":"U","title":"2.4d-Matrices-of-Linear-Maps-solution"},"subContentId":"62317feb-4ffe-4332-8d32-304c8565e893"},"useSeparator":"auto"}]}