To find [tex]\( A - B \)[/tex], we need to subtract each corresponding element of matrix [tex]\( B \)[/tex] from matrix [tex]\( A \)[/tex].
Given:
[tex]\[ A = \begin{pmatrix}
6 & -2 \\
3 & 0 \\
-5 & 4
\end{pmatrix} \][/tex]
and
[tex]\[ B = \begin{pmatrix}
4 & 3 \\
-7 & -4 \\
-1 & 0
\end{pmatrix} \][/tex]
Let's compute the subtraction element-wise:
For the first row:
- The first element: [tex]\( 6 - 4 = 2 \)[/tex]
- The second element: [tex]\( -2 - 3 = -5 \)[/tex]
So, the first row of [tex]\( A - B \)[/tex] is [tex]\([2, -5]\)[/tex].
For the second row:
- The first element: [tex]\( 3 - (-7) = 3 + 7 = 10 \)[/tex]
- The second element: [tex]\( 0 - (-4) = 0 + 4 = 4 \)[/tex]
So, the second row of [tex]\( A - B \)[/tex] is [tex]\([10, 4]\)[/tex].
For the third row:
- The first element: [tex]\( -5 - (-1) = -5 + 1 = -4 \)[/tex]
- The second element: [tex]\( 4 - 0 = 4 \)[/tex]
So, the third row of [tex]\( A - B \)[/tex] is [tex]\([-4, 4]\)[/tex].
Combining all rows, we get:
[tex]\[ A - B = \begin{pmatrix}
2 & -5 \\
10 & 4 \\
-4 & 4
\end{pmatrix} \][/tex]
Therefore, the correct answer is:
[tex]\[ \begin{pmatrix}
2 & -5 \\
10 & 4 \\
-4 & 4
\end{pmatrix} \][/tex]
Which corresponds to the third option:
[tex]\[ \left[\begin{array}{cc}2 & -5 \\ 10 & 4 \\ -4 & 4\end{array}\right] \][/tex]
So, the answer is Option 3.
