Answer :
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]
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]
