Question: If the matrices A and B are symmetric and B is invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well?A+B.
The Matrix A + B is symmetric.
A square matrix is symmetric matrix if
Given that A and B are symmetric matrices and B is invertible.
Since A is symmetric, then .
Then by properties of transpose, it gives,
Therefore, A + B is a symmetric matrix.
Consider a linear transformation L from to that preserves length. What can you say about the kernel of L? What is the dimension of the image? What can you say about the relationship between n and m? If A is the matrix of L, What can you say about the columns of A? What is ? What about ? Illustrate your answer with an example where m=2 and n=3.
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