Consider the following two matrices. Why can't the product of the following two matrices be found? A=begin{bmatrix}-1 & 2&3 4 & 0&5 end{bmatrix} text{ and } B=begin{bmatrix}5 & 2 7 & -8 end{bmatrix}

Question
Matrices
asked 2021-02-25
Consider the following two matrices. Why can't the product of the following two matrices be found? \(A=\begin{bmatrix}-1 & 2&3 \\4 & 0&5 \end{bmatrix} \text{ and } B=\begin{bmatrix}5 & 2 \\7 & -8 \end{bmatrix}\)

Answers (1)

2021-02-26
Step 1
A=\begin{bmatrix}-1 & 2&3 \\4 & 0&5 \end{bmatrix} \text{ and } B=\begin{bmatrix}5 & 2 \\7 & -8 \end{bmatrix}
We explain why matrix product is not possible.
Step 2
If A is a matrix of order \(m \times n\) and B is a matrix of order \(p \times q\)
The matrix product AB is possible if
n=p
Here A is a matrix of order \(2 \times 3 (m \times n)\)
B is a matrix of order \(2 \times 2 (p \times q)\)
Here m=2,n=3,p=2,q=2
Here \(n=3 \neq p=2\)
Since \(n \neq p\) so matrix product not possible
0

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