Given the matrices A = \( \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{bmatrix} \) and B = \( \begin{bmatrix} 3 & 2 & 1 \\ 6 & 5 & 4 \\ 9 & 8 & 7 \\ \end{bmatrix} \). Find the result of the operation 2A + 3B.
Answer
Then, we add the two resulting matrices together. The resulting matrix will have the elements (2A + 3B)ij = (2A)ij + (3B)ij for all i, j. This gives us \( \begin{bmatrix} 11 & 10 & 9 \\ 26 & 25 & 24 \\ 41 & 40 & 39 \\ \end{bmatrix} \)
Step 1 ：First, we multiply each matrix by their respective constants. For matrix A, we have 2A = \( \begin{bmatrix} 2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18 \\ \end{bmatrix} \) and for matrix B we have 3B = \( \begin{bmatrix} 9 & 6 & 3 \\ 18 & 15 & 12 \\ 27 & 24 & 21 \\ \end{bmatrix} \)
Step 2 ：Then, we add the two resulting matrices together. The resulting matrix will have the elements (2A + 3B)ij = (2A)ij + (3B)ij for all i, j. This gives us \( \begin{bmatrix} 11 & 10 & 9 \\ 26 & 25 & 24 \\ 41 & 40 & 39 \\ \end{bmatrix} \)
