Given the matrices AA and BB shown below, find B, minus, A, .B−A.

Question

A, equals, open square bracket,
begin matrix
row 1, column 1, minus, 1
row 1, column 2, 0
row 1, column 3, 3
row 2, column 1, minus, 5
row 2, column 2, 3
row 2, column 3, 5
row 3, column 1, 5
row 3, column 2, minus, 4
row 3, column 3, minus, 3
end matrix
, close square bracket, B, equals, open square bracket,
begin matrix
row 1, column 1, 5
row 1, column 2, minus, 4
row 1, column 3, minus, 2
row 2, column 1, minus, 4
row 2, column 2, minus, 3
row 2, column 3, 3
row 3, column 1, 1
row 3, column 2, minus, 4
row 3, column 3, minus, 1
end matrix
, close square bracket
A=
​

−1
−5
5
​

0
3
−4
​

3
5
−3
​

​
B=
​

5
−4
1
​

−4
−3
−4
​

−2
3
−1
​

​

Answer 1

To find the matrix \( B - A \), we need to subtract each corresponding element of matrix \( A \) from matrix \( B \).

The matrices \( A \) and \( B \) are given as follows:

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

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

Now, we will compute \( B - A \):

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

Calculating each element:

1. First row:

   • \( 5 - (-1) = 5 + 1 = 6 \)
   • \( -4 - 0 = -4 \)
   • \( -2 - 3 = -2 - 3 = -5 \)

2. Second row:

   • \( -4 - (-5) = -4 + 5 = 1 \)
   • \( -3 - 3 = -6 \)
   • \( 3 - 5 = -2 \)

3. Third row:

   • \( 1 - 5 = -4 \)
   • \( -4 - (-4) = -4 + 4 = 0 \)
   • \( -1 - (-3) = -1 + 3 = 2 \)

Putting it all together, we have:

\[ B - A = \begin{bmatrix} 6 & -4 & -5 \ 1 & -6 & -2 \ -4 & 0 & 2 \end{bmatrix} \]

Thus, the result of \( B - A \) is:

\[ \begin{bmatrix} 6 & -4 & -5 \ 1 & -6 & -2 \ -4 & 0 & 2 \end{bmatrix} \]