nicekikah

## Answered question

2020-10-25

Solve for X in the equation, given
$3X+2A=B$

### Answer & Explanation

SkladanH

Skilled2020-10-26Added 80 answers

Step 1
Given that:
The matrix are :

Step 2
Use :
To add or subtract the matrices, they must be the same size as one another. In addition or subtraction of matrices, just add or subtract the corresponding entries in each matrix. To multiply a matrix by some scalar ( that is number ) c, simply multiply each entry in the matrix by c.
Step 3
a) $3X+2A=B.$
To solve the above equation for X:
Let, $3X+2A=B$
Plug the values of matrix A and B in the above equation,
To get, $3X+2A=B$
$3X+2\left[\begin{array}{cc}-4& 0\\ 1& -5\\ -3& 2\end{array}\right]=\left[\begin{array}{cc}1& 2\\ -2& 1\\ 4& 4\end{array}\right]$
Since, $2\left[\begin{array}{cc}-4& 0\\ 1& -5\\ -3& 2\end{array}\right]=\left[\begin{array}{cc}-4\left(2\right)& 0\left(2\right)\\ 1\left(2\right)& -5\left(2\right)\\ -3\left(2\right)& 2\left(2\right)\end{array}\right]$
$=\left[\begin{array}{cc}-8& 0\\ 2& -10\\ -6& 4\end{array}\right]$
Step 4
Plug $2\left[\begin{array}{cc}-4& 0\\ 1& -5\\ -3& 2\end{array}\right]=\left[\begin{array}{cc}-8& 0\\ 2& -10\\ -6& 4\end{array}\right]$ from above equation.
To get ,
$3X+\left[\begin{array}{cc}-8& 0\\ 2& -10\\ -6& 4\end{array}\right]=\left[\begin{array}{cc}1& 2\\ -2& 1\\ 4& 4\end{array}\right]$
Subtract on both side by the matrix $\left[\begin{array}{cc}-8& 0\\ 2& -10\\ -6& 4\end{array}\right]$
$3x=\left[\begin{array}{cc}1& 2\\ -2& 1\\ 4& 4\end{array}\right]-\left[\begin{array}{cc}-8& 0\\ 2& -10\\ -6& 4\end{array}\right]$
$3X=\left[\begin{array}{cc}1-\left(-8\right)& 2-\left(0\right)\\ -2-\left(2\right)& 1-\left(-10\right)\\ 4-\left(-6\right)& 4-4\end{array}\right]$
$3X=\left[\begin{array}{cc}9& 2\\ -4& 11\\ 10& 0\end{array}\right]$
Divide on both side by 3,
To get,
$X=\frac{1}{3}\left[\begin{array}{cc}9& 2\\ -4& 11\\ 10& 0\end{array}\right]$
Therefore
a)$3X+2A=B$
$X=\frac{1}{3}\left[\begin{array}{cc}9& 2\\ -4& 11\\ 10& 0\end{array}\right]$

Jeffrey Jordon

Expert2022-01-27Added 2607 answers

Answer is given below (on video)

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