 # Given the matrices A=begin{bmatrix}5 & 3 -3 & -1 -2 & -5 end{bmatrix} text{ and } B=begin{bmatrix}0 & -2 1 & 3 4 & -3 end{bmatrix} find the 3x2 matrix X that is a solution of the equation. 2X-A=X+B X=? Emeli Hagan 2021-01-30 Answered
Given the matrices

find the 3x2 matrix X that is a solution of the equation. 2X-A=X+B
X=?
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Given
2X-A=X+B
2X-A+A=X+B+A
$⇒2X=X+B+A$
$⇒$ Subtract X from both sides
$2X-X=X+B+A-X\right)$
$⇒X=X-X+B+A$
$⇒X=B+A$
$=\left[\begin{array}{cc}0& -2\\ 1& 3\\ 4& -3\end{array}\right]+\left[\begin{array}{cc}5& 3\\ -3& -1\\ -2& -5\end{array}\right]$
$=\left[\begin{array}{cc}5& -2+3\\ 1-3& 3-1\\ 4-2& -3-5\end{array}\right]$
$=\left[\begin{array}{cc}5& 1\\ -2& 2\\ 2& -8\end{array}\right]$
Step 2
We have used basic matrix addition laws.

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