If the additive inverse of the matrix $\displaystyle \begin{bmatrix}a-2 & b\\ 1 & 3\end{bmatrix}$  is $\displaystyle \begin{bmatrix}2 & 0\\ -1 & -3 \end{bmatrix}$. Find the values of a and b.

Given:

The additive inverse of the matrix $\displaystyle \begin{bmatrix} a-2 & b\\ 1 & 3 \end{bmatrix}$  is $\displaystyle \begin{bmatrix} 2 & 0\\ -1 & -3 \end{bmatrix}$.

To do:

We have to find the values of a and b.

Solution:

We know that,

Additive inverse of a matrix 

$A=\begin{bmatrix} a & b\\ c & d \end{bmatrix}$  is

$-A=\begin{bmatrix} -a & -b\\ -c & -d \end{bmatrix}$.

Given,

A$=\begin{bmatrix} a-2 & b\\ 1 & 3 \end{bmatrix}$

This implies,

$-A\ =\ \begin{bmatrix} -( a-2) & -b\\ -1 & -3 \end{bmatrix}$          

$=\begin{bmatrix} 2 & 0\\ -1 & -3 \end{bmatrix}$                               (given)

Therefore,

$-( a-2)  = 2$

$-a+2=2$

$a=0$

$-b=0$

$b=0$

The values of a and b are 0 and 0 respectively.

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Updated on: 10-Oct-2022

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