Question

1. find -6a - 4b.

a = \\(\

$$\begin{bmatrix}-3 & -3 & -6\\\\ -9 & -2 & 2\\end{bmatrix}$$

\\) b = \\(\

$$\begin{bmatrix}7 & -8 & -5\\\\ -4 & 9 & 1\\end{bmatrix}$$

\\)
a. \\(\

$$\begin{bmatrix}-10 & 60 & 56\\\\ -60 & -46 & -16\\end{bmatrix}$$

\\) c. \\(\

$$\begin{bmatrix}46 & 50 & 16\\\\ 70 & -46 & 22\\end{bmatrix}$$

\\)
b. \\(\

$$\begin{bmatrix}46 & 60 & 56\\\\ 70 & -24 & 22\\end{bmatrix}$$

\\) d. \\(\

$$\begin{bmatrix}-10 & 50 & 56\\\\ 70 & -24 & -16\\end{bmatrix}$$

\\)

1. \\(\

$$\begin{bmatrix}-9 & -1 & 7\\\\ 0 & 9 & 2\\end{bmatrix}$$

+ \

$$\begin{bmatrix}-2 & 0 & 7\\\\ -3 & 5 & -1\\end{bmatrix}$$

\\)
a. \\(\

$$\begin{bmatrix}-11 & 1 & 14\\\\ -3 & 14 & 1\\end{bmatrix}$$

\\) c. \\(\

$$\begin{bmatrix}-11 & 1 & 14\\\\ -3 & 14 & -1\\end{bmatrix}$$

\\)
b. \\(\

$$\begin{bmatrix}-11 & -1 & 14\\\\ -3 & 14 & 1\\end{bmatrix}$$

\\) d. \\(\

$$\begin{bmatrix}-11 & -1 & 14\\\\ 3 & -14 & 1\\end{bmatrix}$$

\\)

1. \\(\

$$\begin{bmatrix}-5 & 2 & 0\\\\ -5 & 9 & 9\\end{bmatrix}$$

• \

$$\begin{bmatrix}-1 & 3 & 3\\\\ 7 & 4 & 7\\end{bmatrix}$$

\\)
a. \\(\

$$\begin{bmatrix}-4 & -1 & -3\\\\ 12 & -5 & 2\\end{bmatrix}$$

\\) c. \\(\

$$\begin{bmatrix}-4 & -1 & -3\\\\ -12 & 5 & 2\\end{bmatrix}$$

\\)
b. \\(\

$$\begin{bmatrix}-4 & -1 & 3\\\\ -12 & 5 & 2\\end{bmatrix}$$

\\) d. \\(\

$$\begin{bmatrix}-4 & 1 & -3\\\\ -12 & 5 & 2\\end{bmatrix}$$

\\)

1. \\(\

$$\begin{bmatrix}-3 & 0\\\\ 5 & -7\\end{bmatrix}$$

+ \

$$\begin{bmatrix}-4 & 2\\\\ -1 & 8\\end{bmatrix}$$

\\)
a. \\(\

$$\begin{bmatrix}-1 & 2\\\\ -4 & 1\\end{bmatrix}$$

\\) c. \\(\

$$\begin{bmatrix}-7 & 2\\\\ 4 & 1\\end{bmatrix}$$

\\)
b. \\(\

$$\begin{bmatrix}-7 & -2\\\\ 4 & -15\\end{bmatrix}$$

\\) d. \\(\

$$\begin{bmatrix}-7 & 2\\\\ 4 & -1\\end{bmatrix}$$

\\)

Explanation:

Problem 94

Step1: Calculate -6A

Multiply each element of matrix \( A =

$$\begin{bmatrix}-3&-3&-6\\-9&-2&2\end{bmatrix}$$

\) by -6:
\( -6A =

$$\begin{bmatrix}-6\times(-3)&-6\times(-3)&-6\times(-6)\\-6\times(-9)&-6\times(-2)&-6\times2\end{bmatrix}$$

=

$$\begin{bmatrix}18&18&36\\54&12&-12\end{bmatrix}$$

\)

Step2: Calculate -4B

Multiply each element of matrix \( B =

$$\begin{bmatrix}7&-8&-5\\-4&9&1\end{bmatrix}$$

\) by -4:
\( -4B =

$$\begin{bmatrix}-4\times7&-4\times(-8)&-4\times(-5)\\-4\times(-4)&-4\times9&-4\times1\end{bmatrix}$$

=

$$\begin{bmatrix}-28&32&20\\16&-36&-4\end{bmatrix}$$

\)

Step3: Add -6A and -4B

Add the corresponding elements of -6A and -4B:
\( -6A - 4B = -6A + (-4B) =

$$\begin{bmatrix}18+(-28)&18 + 32&36+20\\54+16&12+(-36)&-12+(-4)\end{bmatrix}$$

=

$$\begin{bmatrix}-10&50&56\\70&-24&-16\end{bmatrix}$$

\) Wait, wait, no, wait the original operation is -6A - 4B, so actually it's -6A + (-4B)? Wait no, the problem is -6A - 4B, so it's (-6A) + (-4B)? Wait no, -6A -4B is equal to -6A + (-4B). Wait but let's recalculate -6A:

Wait \( A =

$$\begin{bmatrix}-3&-3&-6\\-9&-2&2\end{bmatrix}$$

\), so -6A:

First row: -6(-3)=18, -6(-3)=18, -6*(-6)=36

Second row: -6(-9)=54, -6(-2)=12, -6*2=-12

Then -4B: \( B =

$$\begin{bmatrix}7&-8&-5\\-4&9&1\end{bmatrix}$$

\), so -4B:

First row: -47=-28, -4(-8)=32, -4*(-5)=20

Second row: -4(-4)=16, -49=-36, -4*1=-4

Now add -6A and -4B:

First row: 18 + (-28) = -10; 18 + 32 = 50; 36 + 20 = 56

Second row: 54 + 16 = 70; 12 + (-36) = -24; -12 + (-4) = -16

So the matrix is \(

$$\begin{bmatrix}-10&50&56\\70&-24&-16\end{bmatrix}$$

\), which matches option d.

Step1: Add corresponding elements

For matrices \(

$$\begin{bmatrix}-9&-1&7\\0&9&2\end{bmatrix}$$

\) and \(

$$\begin{bmatrix}-2&0&7\\-3&5&-1\end{bmatrix}$$

\), add element - by - element:

First row: -9 + (-2) = -11; -1 + 0 = -1; 7 + 7 = 14

Second row: 0 + (-3) = -3; 9 + 5 = 14; 2 + (-1) = 1

So the resulting matrix is \(

$$\begin{bmatrix}-11&-1&14\\-3&14&1\end{bmatrix}$$

\), which matches option b.

Step1: Subtract corresponding elements

For matrices \(

$$\begin{bmatrix}-5&2&0\\-5&9&9\end{bmatrix}$$

\) and \(

$$\begin{bmatrix}-1&3&3\\7&4&7\end{bmatrix}$$

\), subtract the second matrix from the first:

First row: -5 - (-1) = -4; 2 - 3 = -1; 0 - 3 = -3

Second row: -5 - 7 = -12; 9 - 4 = 5; 9 - 7 = 2

So the resulting matrix is \(

$$\begin{bmatrix}-4&-1&-3\\-12&5&2\end{bmatrix}$$

\), which matches option c.

Answer:

d. \(

$$\begin{bmatrix}-10&50&56\\70&-24&-16\end{bmatrix}$$

\)

Problem 95