Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.