91Ó°ÊÓ

Find the size of \(A B\) in each case if the matrices can be multiplied. \(A\) has size \(3 \times 2, B\) has size \(2 \times 5\)

For each given matrix \(A,\) show that \(A I=A\) and \(I A=A\) where \(I\) is the identity matrix of the appropriate size. $$A=\left[\begin{array}{ll}1 & 3 \\ 4 & 6\end{array}\right]$$

Find the determinant of each matrix. $$\left[\begin{array}{ll} 1 & 3 \\ 0 & 2 \end{array}\right]$$

Find the determinant of each matrix. $$\left[\begin{array}{rr} 0 & 4 \\ 2 & -1 \end{array}\right]$$

For each given matrix \(A,\) show that \(A I=A\) and \(I A=A\) where \(I\) is the identity matrix of the appropriate size. $$A=\left[\begin{array}{ll}3 & 2 \\ 5 & 9\end{array}\right]$$

Find the size of \(A B\) in each case if the matrices can be multiplied. \(A\) has size \(3 \times 1, B\) has size \(1 \times 3\)

Determine the values of \(x, y,\) and \(z\) that make each matrix equation true. $$\left[\begin{array}{l} 2 z \\ 5 x \end{array}\right]=\left[\begin{array}{r} -1 \\ 2 \end{array}\right]$$

For each given matrix \(A,\) show that \(A I=A\) and \(I A=A\) where \(I\) is the identity matrix of the appropriate size. $$A=\left[\begin{array}{lll}3 & 2 & 1 \\ 5 & 6 & 2 \\ 7 & 8 & 3\end{array}\right]$$

Fill in the blank. The ______ of a matrix is the number of rows and columns in the matrix.

Determine the values of \(x, y,\) and \(z\) that make each matrix equation true. $$\left[\begin{array}{cc} 2 x & 4 y \\ 3 z & 8 \end{array}\right]=\left[\begin{array}{cc} 6 & 16 \\ z+y & 8 \end{array}\right]$$