Question

What are the dimensions of the product?

Answer 1

Answer:

2 x 2

Step-by-step explanation:

Dimensions: m x n

m = number of rows

n = number of columns

When multiplying two matrices:

m x n *  n x k = m x k

MATIX 1:

m = number of rows

n = number of columns

MATRIX 2:

n = number of rows

k = number of columns

RESULTING MATIX:

m = number of rows

k = number of columns

2 x 3 * 3 x 2 = 2 x 2

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

The given matrix multiplication is

$\begin{bmatrix}2&4&-3\\ 6&1&0\end{bmatrix}\times \begin{bmatrix}-3&2\\ -2&3\\ -8&5\end{bmatrix}$

Order of matrix = Number of rows × Number of columns

Let $A=\begin{bmatrix}2&4&-3\\ 6&1&0\end{bmatrix},B=\begin{bmatrix}-3&2\\ -2&3\\ -8&5\end{bmatrix}$

Order of matrix A = 2 × 3

Order of matrix B = 3 × 2

The order of product of two matrices is

$A_{m\times n}\cdot B_{n\times k}=AB_{m\times k}$

It means

Order of product = Number of rows of first matrix × Number of columns of second matrix

Order of product = 2 × 2

$A_{2\times 3}\cdot B_{3\times 2}=AB_{2\times 2}$

The dimensions of the product are 2 × 2. Therefore the correct option is 2.