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[tex]\[
A=\left[\begin{array}{cccc}
-3 & 1 & 0 & 7 \\
5 & -6 & 1 & 3 \\
8 & 2 & 6 & -5
\end{array}\right] \quad B=\left[\begin{array}{cccc}
5 & 3 & -7 & -5 \\
0 & 1 & 6 & -6 \\
5 & -4 & 9 & 3
\end{array}\right]
\][/tex]

The elements of [tex]\(A+B\)[/tex] are represented by [tex]\(x_{ij}\)[/tex] and the elements of [tex]\(A-B\)[/tex] are represented by [tex]\(y_{ij}\)[/tex], where [tex]\(i\)[/tex] and [tex]\(j\)[/tex] are whole numbers. So [tex]\(x_{24}\)[/tex] represents the element [tex]\(\square\)[/tex] and [tex]\(y_{13}\)[/tex] represents the element [tex]\(\square\)[/tex].

Sagot :

GinnyAnsweridn
To find the elements of the matrices [tex]\(A + B\)[/tex] and [tex]\(A - B\)[/tex], we need to perform matrix addition and subtraction.

Matrix [tex]\(A\)[/tex] and matrix [tex]\(B\)[/tex] are given as:
[tex]\[ A = \begin{pmatrix} -3 & 1 & 0 & 7 \\ 5 & -6 & 1 & 3 \\ 8 & 2 & 6 & -5 \end{pmatrix} \][/tex]
[tex]\[ B = \begin{pmatrix} 5 & 3 & -7 & -5 \\ 0 & 1 & 6 & -6 \\ 5 & -4 & 9 & 3 \end{pmatrix} \][/tex]

### Matrix Addition [tex]\(A + B\)[/tex]:

To add two matrices, we add their corresponding elements:

[tex]\[ A + B = \begin{pmatrix} -3 + 5 & 1 + 3 & 0 + (-7) & 7 + (-5) \\ 5 + 0 & -6 + 1 & 1 + 6 & 3 + (-6) \\ 8 + 5 & 2 + (-4) & 6 + 9 & -5 + 3 \end{pmatrix} \][/tex]

[tex]\[ A + B = \begin{pmatrix} 2 & 4 & -7 & 2 \\ 5 & -5 & 7 & -3 \\ 13 & -2 & 15 & -2 \end{pmatrix} \][/tex]

Here, [tex]\(x_{24}\)[/tex] represents the element in the 2nd row and 4th column of [tex]\(A + B\)[/tex]. So,
[tex]\[ x_{24} = -3 \][/tex]

### Matrix Subtraction [tex]\(A - B\)[/tex]:

To subtract two matrices, we subtract their corresponding elements:

[tex]\[ A - B = \begin{pmatrix} -3 - 5 & 1 - 3 & 0 - (-7) & 7 - (-5) \\ 5 - 0 & -6 - 1 & 1 - 6 & 3 - (-6) \\ 8 - 5 & 2 - (-4) & 6 - 9 & -5 - 3 \end{pmatrix} \][/tex]

[tex]\[ A - B = \begin{pmatrix} -8 & -2 & 7 & 12 \\ 5 & -7 & -5 & 9 \\ 3 & 6 & -3 & -8 \end{pmatrix} \][/tex]

Here, [tex]\(y_{13}\)[/tex] represents the element in the 1st row and 3rd column of [tex]\(A - B\)[/tex]. So,
[tex]\[ y_{13} = 7 \][/tex]

Therefore, [tex]\(x_{24}\)[/tex] represents the element [tex]\(-3\)[/tex] and [tex]\(y_{13}\)[/tex] represents the element [tex]\(7\)[/tex].
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