Question

Find c23 and c11, where c = 2a − 3b, a = 5 3 3 −2 4 1 , and b = 1 2 −7 0 −5 1 .

Answer 1

To calculate c23 and c11, we first multiply matrices a and b by 2 and -3, respectively, then subtract the resulting matrices. The value of c23 is 27, and the value of c11 is 7.

Step-by-step explanation:

To find the matrix elements c23 and c11, where c = 2a - 3b, and matrices a and b are given, we first perform the matrix multiplication by the scalar for each matrix and then subtract one from the other as per the matrix subtraction rule.

First, let's find the matrices after scalar multiplication:

2a =

2 × a = 2 × [5, 3, 3; -2, 4, 1] = [10, 6, 6; -4, 8, 2]

3b =

3 × b = 3 × [1, 2, -7; 0, -5, 1] = [3, 6, -21; 0, -15, 3].

Now, we subtract 3b from 2a to get c:

c = 2a - 3b =

[10, 6, 6; -4, 8, 2] - [3, 6, -21; 0, -15, 3] = [7, 0, 27; -4, 23, -1].

Finally, we extract the values of c23 and c11:

c23 = 27 (row 2, column 3)

c11 = 7 (row 1, column 1).