Question

Given the matrices AA and BB shown below, find B, minus, A, .B−A.
A, equals, open square bracket,
begin matrix
row 1, column 1, minus, 3
row 1, column 2, 5
row 1, column 3, 0
row 1, column 4, 2
row 2, column 1, minus, 3
row 2, column 2, 4
row 2, column 3, 0
row 2, column 4, 0
end matrix
, close square bracket, B, equals, open square bracket,
begin matrix
row 1, column 1, minus, 5
row 1, column 2, minus, 2
row 1, column 3, 5
row 1, column 4, minus, 5
row 2, column 1, 4
row 2, column 2, minus, 5
row 2, column 3, minus, 2
row 2, column 4, minus, 1
end matrix
, close square bracket
A=[
−3
−3
​

5
4
​

0
0
​

2
0
​
]B=[
−5
4
​

−2
−5
​

5
−2
​

−5
−1
​
]

Answer 1

To find the matrix \( B - A \), we first need to subtract the corresponding elements of matrix \( A \) from matrix \( B \). Given the matrices:

\[
A = \begin{bmatrix}
-3 & 5 & 0 & 2 \\
-3 & 4 & 0 & 0
\end{bmatrix}
\]

\[
B = \begin{bmatrix}
-5 & -2 & 5 & -5 \\
4 & -5 & -2 & -1
\end{bmatrix}
\]

We'll perform the element-wise subtraction for each position in the matrices.

### Calculation

**For the first row:**
1. First column: \( -5 - (-3) = -5 + 3 = -2 \)
2. Second column: \( -2 - 5 = -7 \)
3. Third column: \( 5 - 0 = 5 \)
4. Fourth column: \( -5 - 2 = -7 \)

**For the second row:**
1. First column: \( 4 - (-3) = 4 + 3 = 7 \)
2. Second column: \( -5 - 4 = -9 \)
3. Third column: \( -2 - 0 = -2 \)
4. Fourth column: \( -1 - 0 = -1 \)

### Putting it all together

Now, we can write the result of \( B - A \):

\[
B - A = \begin{bmatrix}
-2 & -7 & 5 & -7 \\
7 & -9 & -2 & -1
\end{bmatrix}
\]

Thus, the final result is:

\[
B - A = \begin{bmatrix}
-2 & -7 & 5 & -7 \\
7 & -9 & -2 & -1
\end{bmatrix}
\]