Matrices

Practice Questions

Linear Algebra › Matrices

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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 .

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

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 .

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

Find .

Compute $A\cdot B$ , where

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

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

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

Calculate $A ^{50}$ .

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

Calculate $A ^{50}$ .

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?

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 $A\cdot B$ ?

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