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Find the difference.

[tex]\[
\left[\begin{array}{cc}
-11 & 4 \\
3 & -2 \\
-10 & 13
\end{array}\right] - \left[\begin{array}{cc}
1 & 2 \\
1 & 3 \\
-2 & 6
\end{array}\right]
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's find the difference between the two matrices by subtracting corresponding elements step-by-step.

We are given two matrices:

Matrix [tex]\( A \)[/tex]:
[tex]\[ \begin{pmatrix} -11 & 4 \\ 3 & -2 \\ -10 & 13 \end{pmatrix} \][/tex]

Matrix [tex]\( B \)[/tex]:
[tex]\[ \begin{pmatrix} 1 & 2 \\ 1 & 3 \\ -2 & 6 \end{pmatrix} \][/tex]

To find the difference [tex]\( A - B \)[/tex], we subtract each element of matrix [tex]\( B \)[/tex] from the corresponding element of matrix [tex]\( A \)[/tex].

Let's perform the subtraction element by element:

First row:
[tex]\[ \begin{pmatrix} -11 - 1 & 4 - 2 \end{pmatrix} = \begin{pmatrix} -12 & 2 \end{pmatrix} \][/tex]

Second row:
[tex]\[ \begin{pmatrix} 3 - 1 & -2 - 3 \end{pmatrix} = \begin{pmatrix} 2 & -5 \end{pmatrix} \][/tex]

Third row:
[tex]\[ \begin{pmatrix} -10 - (-2) & 13 - 6 \end{pmatrix} = \begin{pmatrix} -8 & 7 \end{pmatrix} \][/tex]

Combining all the rows together, the difference matrix [tex]\( A - B \)[/tex] is:
[tex]\[ \begin{pmatrix} -12 & 2 \\ 2 & -5 \\ -8 & 7 \end{pmatrix} \][/tex]

Thus, the result of the subtraction is:
[tex]\[ \begin{pmatrix} -12 & 2 \\ 2 & -5 \\ -8 & 7 \end{pmatrix} \][/tex]
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