# Given B=begin{bmatrix}-3 & -3 1 & -2 end{bmatrix} text{ and } C=begin{bmatrix}-15 & -6 1 & 10 end{bmatrix} Solve 3X+B=C X=?

Given
Solve $3X+B=C$
X=?
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Willie
Step 1
Given :
The matrices

To solve :
The matrix 3 X + B = C for X
Step 2
Given :
The matrices
Let
3X+B=C
$\left[\begin{array}{cc}3a& 3b\\ 3c& 3d\end{array}\right]+\left[\begin{array}{cc}-3& -3\\ 1& -2\end{array}\right]=\left[\begin{array}{cc}-15& -6\\ 1& 10\end{array}\right]$
$\left[\begin{array}{cc}3a-3& 3b-3\\ 3c+1& 3d-2\end{array}\right]=\left[\begin{array}{cc}-15& -6\\ 1& 10\end{array}\right]$
Equating each element of the matrix , we have
$3a-3=-15$
$3a=-15+3$
$3a=-12$
$a=\frac{-12}{3}$
$a=-4$
$3b-3=-6$
$3b=-6+3$
$3b=-3$
$b=-1$
$3c+1=1$
$3c=1-1$
$3c=0$
$c=0$
$3d-2=10$
$3d=10+2$
$3d=12$
$d=\frac{12}{3}$
$d=4$
Therefore,
$X=\left[\begin{array}{cc}-4& -1\\ 0& 4\end{array}\right]$
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