To solve the given matrix problem, we need to perform two main steps: multiplying the first matrix by [tex]\(-1\)[/tex] and then adding the resulting matrix to the second matrix. Here is a detailed, step-by-step solution:
Step 1: Multiply the first matrix by [tex]\(-1\)[/tex].
The first matrix is:
[tex]\[
\left[\begin{array}{rr}
2 & 6 \\
-2 & 5 \\
0 & 8
\end{array}\right]
\][/tex]
Multiplying each element of this matrix by [tex]\(-1\)[/tex] gives us:
[tex]\[
(-1) \times \left[\begin{array}{rr}
2 & 6 \\
-2 & 5 \\
0 & 8
\end{array}\right] = \left[\begin{array}{rr}
-2 & -6 \\
2 & -5 \\
0 & -8
\end{array}\right]
\][/tex]
Step 2: Add the resulting matrix to the second matrix.
The second matrix is:
[tex]\[
\left[\begin{array}{cc}
1 & 8 \\
0 & -1 \\
6 & 3
\end{array}\right]
\][/tex]
We now add the matrices element by element:
[tex]\[
\left[\begin{array}{rr}
-2 & -6 \\
2 & -5 \\
0 & -8
\end{array}\right] + \left[\begin{array}{cc}
1 & 8 \\
0 & -1 \\
6 & 3
\end{array}\right] = \left[\begin{array}{cc}
(-2+1) & (-6+8) \\
(2+0) & (-5-1) \\
(0+6) & (-8+3)
\end{array}\right]
\][/tex]
Performing the addition for each corresponding element, we get:
[tex]\[
\left[\begin{array}{cc}
-1 & 2 \\
2 & -6 \\
6 & -5
\end{array}\right]
\][/tex]
Therefore, the resulting matrix after performing the given operations is:
[tex]\[
\left[\begin{array}{cc}
-1 & 2 \\
2 & -6 \\
6 & -5
\end{array}\right]
\][/tex]
