aortiH

2020-12-25

The $2×2$ matrices A and B below are related to matrix C by the equation: $C=3A-2B$. Which of the following is matrix C.
$A=\left[\begin{array}{cc}3& 5\\ -2& 1\end{array}\right]B=\left[\begin{array}{cc}-4& 5\\ 2& 1\end{array}\right]$
$\left[\begin{array}{cc}-1& 5\\ 2& 1\end{array}\right]$
$\left[\begin{array}{cc}-18& 5\\ 10& 1\end{array}\right]$
$\left[\begin{array}{cc}18& -5\\ -10& -1\end{array}\right]$
$\left[\begin{array}{cc}1& -5\\ -2& -1\end{array}\right]$

### Answer & Explanation

casincal

Step 1
We have to find matrix C by the equation C=3A−2B where matrices are given as:

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
$C=3A-2B$
$=3\left[\begin{array}{cc}3& 5\\ -2& 1\end{array}\right]-2\left[\begin{array}{cc}-4& 5\\ 2& 1\end{array}\right]$
$=\left[\begin{array}{cc}3×3& 3×5\\ 3×\left(-2\right)& 3×1\end{array}\right]-\left[\begin{array}{cc}2×\left(-4\right)& 2×5\\ 2×2& 2×1\end{array}\right]$
$=\left[\begin{array}{cc}9& 15\\ -6& 3\end{array}\right]-\left[\begin{array}{cc}-8& 10\\ 4& 2\end{array}\right]$
$=\left[\begin{array}{cc}9-\left(-8\right)& 15-10\\ -6-4& 3-2\end{array}\right]$
$=\left[\begin{array}{cc}9+8& 5\\ -10& 1\end{array}\right]$
$=\left[\begin{array}{cc}17& 5\\ -10& 1\end{array}\right]$
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.

Jeffrey Jordon

Answer is given below (on video)

Jeffrey Jordon