Answer:
To find the matrices A + B and A - B, we need to add and subtract the corresponding elements of matrices A and B. Given A = [6 4; 0 8; 8 -9] and B = [9; 5; 4], let's perform the matrix operations: a. A + B: To add two matrices, we add their corresponding elements. In this case, we have: A + B = [6+9 4+9; 0+5 8+5; 8+4 -9+4] = [15 13; 5 13; 12 -5] b. A - B: To subtract two matrices, we subtract their corresponding elements. In this case, we have: A - B = [6-9 4-9; 0-5 8-5; 8-4 -9-4] = [-3 -5; -5 3; 4 -13] c. -9A: To multiply a matrix by a scalar, we multiply each element of the matrix by that scalar. In this case, we have: -9A = -9 * [6 4; 0 8; 8 -9] = [-54 -36; 0 -72; -72 81] d. 5A + 4B: To perform this operation, we need to first multiply matrix A by scalar 5, then multiply matrix B by scalar 4, and finally add the resulting matrices together. In this case, we have: 5A = 5 * [6 4; 0 8; 8 -9] = [30 20; 0 40; 40 -45] 4B = 4 * [9; 5; 4] = [36; 20; 16] 5A + 4B = [30+36 20+36; 0+20 40+20; 40+16 -45+16] = [66 56; 20 60; 56 -29] In conclusion: a. A + B = [15 13; 5 13; 12 -5] b. A - B = [-3 -5; -5 3; 4 -13] c. -9A = [-54 -36; 0 -72; -72 81] d. 5A + 4B = [66 56; 20 60; 56 -29] Please note that these calculations are based on the given matrices A and B.
Explanation: