aortiH

2020-12-25

The

casincal

Skilled2020-12-26Added 82 answers

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.

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:

Now for addition we add corresponding elements,

Step 2

Applying above rule for the given condition, we get

Hence, value of C is

Note:

There is no suitable option for the given conditions.

Jeffrey Jordon

Expert2022-01-27Added 2575 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-08-23Added 2575 answers