Question

Subtract the matrices. What number fills in [?] ? B 9 -3 5 A - B= -2 15 -3 -8 14 [?]

Answer 1

`\stackrel{ \textit{\LARGE A} }{\begin{bmatrix} 2&9&-4\\ -3&5&1 \end{bmatrix}}\hspace{5em} \stackrel{ \textit{\LARGE B} }{\begin{bmatrix} 4&-6&-1\\ 5&-9&4 \end{bmatrix}} \\\\[-0.35em] ~\dotfill\\\\ A-B\implies \begin{bmatrix} \boxed{2-4}&\boxed{9-(-6)}&\boxed{-4-(-1)}\\\\ \boxed{-3-5}&\boxed{5-(-9)}&\boxed{1-4} \end{bmatrix}\implies \begin{bmatrix} -2&15&-3\\ -8&14&-3 \end{bmatrix}`

Answer 2

To subtract two matrices, you simply subtract corresponding elements from each other. Given matrices A and B, the resulting matrix C (A - B) will have elements where each element of A is subtracted from the corresponding element of B.

Matrix A:
```
9 -3
5 1
```

Matrix B:
```
-2 15
-3 -8
```

Subtracting B from A element-wise:
```
(9 - (-2)) (-3 - 15)
(5 - (-3)) (1 - (-8))
```

Calculating these values:
```
(9 + 2) (-3 - 15)
(5 + 3) (1 + 8)
```

```
11 -18
8 9
```

So, the resulting matrix C = A - B is:
```
11 -18
8 9
```

The missing element in the matrix you provided should be 11.