Matrix-Matrix Product

Practice Questions

Linear Algebra › Matrix-Matrix Product

Page 1 of 11

10 of 103

Let $A = \begin{bmatrix} \frac{2}{5} & \frac{1}{4}\end{bmatrix}$ and $B = \begin{bmatrix} \frac{3}{2} & \frac{1}{4} \ \ \frac{3}{4} &- \frac{1}{5}\end{bmatrix}$ .

Find .

Let $A = \begin{bmatrix} 2\sqrt{2} & \sqrt{3} \end{bmatrix}$ and $B = \begin{bmatrix} \sqrt{2} & \sqrt{6} \-2 \sqrt{6} & \sqrt{3} \end{bmatrix}$ .

Find .

What is dimension criteria to multiply two matrices $(A\times B)$ ?

True or false: A matrix whose determinant is neither 0 nor 1 cannot be an idempotent matrix.

For any given value , how many $n \times n$ nonsingular idempotent matrices exist?

Compute $A\cdot B$ , where

$A=\begin{bmatrix}8&4 \ 2&4 \ 6&1 \end{bmatrix}$ $b=\begin{bmatrix}4&2 \ 4&9 \ 2&1 \end{bmatrix}$

is a $2 \times 2$ nonsingular matrix; is a $3 \times 2$ matrix; is a $2 \times 2$ singular matrix.

Which of the following is defined?

$A = \begin{bmatrix} \frac{1}{4} & \frac{\sqrt{3}}{4} \ \ \frac{\sqrt{3}}{4} & \frac{3}{4} \end{bmatrix}$

True or false:

is an example of an idempotent matrix.

Your friend Hector wants to multiply two matrices and as follows: $A\cdot B$ . Unfortunately, Hector knows nothing about matrix dimensions. Which of the following statements will help Hector figure out whether it is possible for him to multiply $A\cdot B$ ?

$A = \begin{bmatrix} 1 & 0 \ 1 &1 \end{bmatrix}$

Calculate $A ^{50}$ .

Page 1 of 11

Return to subject