Find if possible the matrices: a) AB b) BA A=[−1−2−3],B=[123]

Question: "Find if possible the matrices: a) AB b)..."

babeeb0oL

Answered question

2021-01-02

Find if possible the matrices:
a) AB
b) BA

A = [\begin{matrix} - 1 \\ - 2 \\ - 3 \end{matrix}], B = [\begin{matrix} 1 & 2 & 3 \end{matrix}]

Answer & Explanation

broliY

Skilled2021-01-03Added 97 answers

Step 1
Given that:
The matrices,
$A = [\begin{matrix} - 1 \\ - 2 \\ - 3 \end{matrix}], B = [\begin{matrix} 1 & 2 & 3 \end{matrix}]$
Step 2
We know that,
Finding the product of two matrices is only possible when the inner dimension are same , meaning that the number of columns of the first matrix is equal to the number of rows of the second matrix.
a) To find AB :
Let, $A = [\begin{matrix} - 1 \\ - 2 \\ - 3 \end{matrix}], B = [\begin{matrix} 1 & 2 & 3 \end{matrix}]$
Number of columns of first matrix (A) is 1 .
Number of rows of the second matrix is 1.
To get,
Step 3
Number of columns of $A =$ Number of rows of $B = 1$ .
Then,
$A B = [\begin{matrix} - 1 \\ - 2 \\ - 3 \end{matrix}] [\begin{matrix} 1 & 2 & 3 \end{matrix}] = [\begin{matrix} - 1 (1) & (- 2) (2) & (- 3) (3) \end{matrix}] = [\begin{matrix} - 1 & - 4 & - 9 \end{matrix}]$
To get,
$A B = [\begin{matrix} - 1 & - 4 & - 9 \end{matrix}]$
b) To find BA :
Number of columns of first matrix B is 3 and number of rows of matrix A is 3 which are equal .
Then,
Step 4
$B A = [\begin{matrix} 1 & 2 & 3 \end{matrix}] [\begin{matrix} - 1 \\ - 2 \\ - 3 \end{matrix}] = [\begin{matrix} 1 (- 1) + 2 (- 2) + 3 (- 3) \end{matrix}] = [\begin{matrix} - 1 - 4 - 9 \end{matrix}] = [\begin{matrix} - 14 \end{matrix}]$
Therefore,
a) $A B = [\begin{matrix} - 1 - 4 - 9 \end{matrix}]$
b) $B A = [\begin{matrix} - 14 \end{matrix}]$

Jeffrey Jordon

Expert2022-01-22Added 2605 answers

Answer is given below (on video)

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