Suppose that Lis symmetric n xn matrix and Ris any n x n matrix (not necessarily symmetric). Which of the following matrices must symmetric? (6) R" R (ii) LRT + RL (ii) (-2R)" LR

Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.

Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be used to create a leading 1 at the top of the first column. Which do you prefer and why?

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.