Answer:
To perform these operations, we need to ensure that the dimensions of the matrices match. Since k is a row matrix with 1 row and 4 columns, and L is a column matrix with 4 rows and 1 column, we need to transpose one of them to match the dimensions. Let's transpose k to get a column matrix with 4 rows and 1 column:
k^T = 2
3
4
3
Now we can perform the matrix operations:
1. k + L:
2 + 7 = 9 3 + 10 = 13 4 + 5 = 9 3 + 11 = 14
9 + 1 = 10 13 + 6 = 19 5 + 9 = 14 11 + 4 = 15
10 + 11 = 21 4 + 7 = 11 7 + 10 = 17 3 + 7 = 10
= 9 13 9 14
10 19 14 15
21 11 17 10
2. K - L:
2 - 7 = -5 3 - 10 = -7 4 - 5 = -1 3 - 11 = -8
9 - 1 = 8 13 - 6 = 7 5 - 9 = -4 11 - 4 = 7
10 - 11 = -1 4 - 7 = -3 7 - 10 = -3 3 - 7 = -4
= -5 -7 -1 -8
8 7 -4 7
-1 -3 -3 -4
3. 2k + 3L:
2(2) + 3(7) = 20 2(3) + 3(10) = 36 2(4) + 3(5) = 22 2(3) + 3(11) = 37
2(9) + 3(1) = 21 2(13) + 3(6) = 44 2(5) + 3(9) = 23 2(11) + 3(4) = 29
2(10) + 3(11) = 42 2(4) + 3(7) = 29 2(7) + 3(10) = 34 2(3) + 3(7) = 23
= 20 36 22 37
21 44 23 29
42 29 34 23
4. 3L - 2K:
3(7) - 2(2) = 17 3(10) - 2(3) = 27 3(5) - 2(4) = 7 3(11) - 2(3) = 29
3(1) - 2(9) = -15 3(6) - 2(13) = -11 3(9) - 2(5) = 17 3(4) - 2(11) = -14
3(11) - 2(10) = 13 3(7) - 2(4) = 14 3(10) - 2(7) = 16 3(7) - 2(3) = 15
= 17 27 7 29
-15 -11 17 -14
13 14 16 15