Question

1. which of the following matrix multiplications (products) will result in a matrix with the dimensions of 2x4?

a) a 4x1 matrix with a 1x2 matrix b) a 2x3 matrix with a 3x4 matrix
c) a 2x4 matrix with a 2x4 matrix d) a 3x2 matrix with a 4x3 matrix

1. if a is a 2x5 matrix and b is a 5x3 matrix, what are the dimensions of ab?

a) 5x5 b) 3x2 c) 2x3 d) ab is undefined

1. find the value of x in the matrix equation.

$\

$$\begin{bmatrix}-2 & 4 & 1 \\\\ 0 & -3 & 2\\end{bmatrix}$$

\cdot \

$$\begin{bmatrix}-2 & -1 \\\\ 3 & 4 \\\\ -2 & 2\\end{bmatrix}$$

= \

$$\begin{bmatrix}a & b \\\\ x & c\\end{bmatrix}$$

$
answer:

1. what is the missing value of x that makes the matrix equation true?

$\

$$\begin{bmatrix}4 & -5 \\\\ 1 & 2\\end{bmatrix}$$

\cdot \

$$\begin{bmatrix}x & 1 \\\\ -2 & 3\\end{bmatrix}$$

= \

$$\begin{bmatrix}-2 & -11 \\\\ -7 & 7\\end{bmatrix}$$

$
answer:

Explanation:

Step1: Recall matrix product dimension rule

For matrices $M_{m \times n}$ and $N_{n \times p}$, product $MN$ is $m \times p$.
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Question 4

Step1: Check each option's dimensions

a) $4 \times 1 \cdot 1 \times 2 = 4 \times 2$
b) $2 \times 3 \cdot 3 \times 4 = 2 \times 4$
c) $2 \times 4 \cdot 2 \times 4$: undefined (inner dim mismatch)
d) $3 \times 2 \cdot 4 \times 3$: undefined (inner dim mismatch)

Question 5

Step1: Apply dimension rule to $A_{2 \times 5}, B_{5 \times 3}$

$AB$ dimensions: $2 \times 3$

Question 6

Step1: Calculate $x$ (2nd row, 1st col of product)

$x = (0)(-2) + (-3)(3) + (2)(-2)$
$x = 0 - 9 - 4$

Question 7

Step1: Set up equation for 1st row,1st col

$4x + (-5)(-2) = -2$

Step2: Solve for $x$

$4x + 10 = -2$
$4x = -12$
$x = \frac{-12}{4}$

Answer:

1. b) A 2x3 matrix with a 3x4 matrix
2. c) 2x3
3. $x = -13$
4. $x = -3$