The 2×2 matrices A and B below are related to matrix C by the equation:...

Step 1
We have to find matrix C by the equation C=3A−2B where matrices are given as:
$A=\left[\begin{array}{cc}3& 5\\ -2& 1\end{array}\right]\text{ and }B=\left[\begin{array}{cc}-4& 5\\ 2& 1\end{array}\right]$
We know the operations of matrices,
If we multiply by any scalar to the matrix then it get multiplied in each elements example:
$2\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=\left[\begin{array}{cc}2a& 2b\\ 2c& 2d\end{array}\right]$
Now for addition we add corresponding elements,
$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]+\left[\begin{array}{cc}x& y\\ z& w\end{array}\right]=\left[\begin{array}{cc}a+x& b+y\\ c+z& d+w\end{array}\right]$
Step 2
Applying above rule for the given condition, we get
$C=3A-2B$
$=3\left[\begin{array}{cc}3& 5\\ -2& 1\end{array}\right]-2\left[\begin{array}{cc}-4& 5\\ 2& 1\end{array}\right]$
$=\left[\begin{array}{cc}3\times 3& 3\times 5\\ 3\times (-2)& 3\times 1\end{array}\right]-\left[\begin{array}{cc}2\times (-4)& 2\times 5\\ 2\times 2& 2\times 1\end{array}\right]$
$=\left[\begin{array}{cc}9& 15\\ -6& 3\end{array}\right]-\left[\begin{array}{cc}-8& 10\\ 4& 2\end{array}\right]$
$=\left[\begin{array}{cc}9-(-8)& 15-10\\ -6-4& 3-2\end{array}\right]$
$=\left[\begin{array}{cc}9+8& 5\\ -10& 1\end{array}\right]$
$=\left[\begin{array}{cc}17& 5\\ -10& 1\end{array}\right]$
Hence, value of C is $\left[\begin{array}{cc}17& 5\\ -10& 1\end{array}\right]$
Note:
There is no suitable option for the given conditions.

Answer is given below (on video)