[amp_mcq option1=”Statement 1 is true but 2 is false” option2=”Statement 1 is false but 2 is true” option3=”Both the statements are true” option4=”Both the statements are false” correct=”option1″]<\/p>\n
The correct answer is: A. Statement 1 is true but 2 is false.<\/strong><\/p>\n Statement 1 is true because the product of a matrix and its transpose is a scalar. This is a property of matrices, and it holds regardless of the specific matrices involved.<\/p>\n Statement 2 is false because the product of a matrix and its transpose is not always symmetric. This is only true if the matrix is symmetric itself. In this case, matrix $D$ is not symmetric, so the product $D^T F D$ is not symmetric.<\/p>\n Here is a more detailed explanation of each statement:<\/p>\n Statement 1:<\/strong> The product of a matrix and its transpose is a scalar. This is a property of matrices, and it holds regardless of the specific matrices involved. For example, if $A$ is a $3\\times3$ matrix and $B$ is a $3\\times3$ matrix, then $A^T B$ is a $3\\times3$ matrix.<\/p>\n<\/li>\n Statement 2:<\/strong> The product of a matrix and its transpose is not always symmetric. This is only true if the matrix is symmetric itself. A symmetric matrix is a matrix that is equal to its transpose. For example, if $A$ is a $3\\times3$ symmetric matrix, then $A^T=A$.<\/p>\n<\/li>\n<\/ul>\n In this case, matrix $D$ is not symmetric. This is because $D$ is a $5\\times3$ matrix, and the only way for a $5\\times3$ matrix to be symmetric is if it is a diagonal matrix. However, matrix $D$ is not a diagonal matrix, so it is not symmetric.<\/p>\n Therefore, the product $D^T F D$ is not symmetric.<\/p>\n","protected":false},"excerpt":{"rendered":" [amp_mcq option1=”Statement 1 is true but 2 is false” option2=”Statement 1 is false but 2 is true” option3=”Both the statements are true” option4=”Both the statements are false” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"class_list":["post-20025","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\n\n