Given [tex]\( A = \left[\begin{array}{cc}6 & -2 \\ 3 & 0 \\ -5 & 4\end{array}\right] \)[/tex] and [tex]\( B = \left[\begin{array}{cc}4 & 3 \\ -7 & -4 \\ -1 & 0\end{array}\right] \)[/tex],

what is [tex]\( A - B \)[/tex]?

A. [tex]\(\left[\begin{array}{cc}10 & 1 \\ -4 & -4 \\ -6 & 4\end{array}\right]\)[/tex]

B. [tex]\(\left[\begin{array}{cc}2 & 1 \\ -4 & -4 \\ -6 & 4\end{array}\right]\)[/tex]

C. [tex]\(\left[\begin{array}{cc}2 & -5 \\ 10 & 4 \\ -4 & 4\end{array}\right]\)[/tex]

D. [tex]\(\left[\begin{array}{cc}-2 & 5 \\ -10 & -4 \\ 4 & -4\end{array}\right]\)[/tex]



Answer :

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.