Question

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

−4
−5
​

1
−4
​
]B=[
2
−5
​

0
2
​

−1
−2
​
]

Answer 1

To find \( A - B \), we need to subtract the corresponding elements of matrices \( A \) and \( B \).

Given:

\[
A = \begin{bmatrix}
-5 & -4 & 1 \\
3 & -5 & -4
\end{bmatrix}, \quad
B = \begin{bmatrix}
2 & 0 & -1 \\
-5 & 2 & -2
\end{bmatrix}
\]

Now we will perform the subtraction \( A - B \):

\[
A - B = \begin{bmatrix}
-5 & -4 & 1 \\
3 & -5 & -4
\end{bmatrix} -
\begin{bmatrix}
2 & 0 & -1 \\
-5 & 2 & -2
\end{bmatrix}
\]

Subtracting the corresponding elements:

1. First row, first column: \(-5 - 2 = -7\)
2. First row, second column: \(-4 - 0 = -4\)
3. First row, third column: \(1 - (-1) = 1 + 1 = 2\)

4. Second row, first column: \(3 - (-5) = 3 + 5 = 8\)
5. Second row, second column: \(-5 - 2 = -7\)
6. Second row, third column: \(-4 - (-2) = -4 + 2 = -2\)

Putting it all together, we get:

\[
A - B = \begin{bmatrix}
-7 & -4 & 2 \\
8 & -7 & -2
\end{bmatrix}
\]

Thus, the resulting matrix \( A - B \) is:

\[
A - B = \begin{bmatrix}
-7 & -4 & 2 \\
8 & -7 & -2
\end{bmatrix}
\]