Question

Perform the following matrix operation. Enter your matrix by row, with entries separated by commas. would be entered as a,b,c,d. 49cdan Do not round your answers. st Save Submit Problem #4 for Grading Attempt #1 | Attempt #2 Attempt #3 Problem #4 Your Answer: Your Mark: Perform the following matrix operation. [1 212 2:] Enter your matrix by row, with entries separated by commas. uld be entered as a,b,c,d,e,f

Answer 1

In the matrix operation, the operator applies to each element of the matrix.

We are given,

$\begin{bmatrix} 4 & 4 \\ 4 & 5 \end{bmatrix}~-~\frac{1}{5}\begin{bmatrix} -5 & 1 \\ 1 & -4 \end{bmatrix}$

Thus, here, in the second matrix, each element would be divided by 5, so we get:

$\begin{bmatrix} 4 & 4 \\ 4 & 5 \end{bmatrix}~-~\begin{bmatrix} -1 & \frac{1}{5} \\ \frac{1}{5} & \frac{-4}{5} \end{bmatrix}$

Now, both matrices are subtracted, in the subtraction rule of the matrix, each element of the matrix subtracted with their corresponding matrix element. So, we get:

4-(-1) 4-1 5-(

On simplifying this we get;

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Thus, the answer is:   Answer

حات

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4 21 「-2 2| |-4 -3 2 -5 3

Here, we can see that both matrices are in multiplication.

The rule for multiplication of matrices is: Each row of the first matrix is multiplied with the corresponding column of the second matrix.

That First row of the first matrix multiplies with the corresponding element of the first column of second matrix, again, the first row of the first matrix multiplies with the corresponding element of the second column of the second matrix and so on. Then the second row of the first matrix multiplies with the corresponding element of the first column of the second matrix, again the second row of the first matrix multiplies with the corresponding element of the second column of the second matrix and so on.

[4 ]「-2 2 |-4 -3 2 -5 3 「4+ (-2)+2+(-4) | 2 *(-2)+2+(-4) 4+ (-3)+2+2 2+(-3)+2+2 4+(-5)+2+3 2+(-5)+2+3||

* [-2 -3 12 2'1-4 2 -5 31 -12+4 - +4 8 -20 + 6 -10+6

「-2 2| |-4 -3 2 -5 3 -14] —2 -4||

Hence, the answer is:

—16, -8, -14 -12 -2 -4

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