operations with matrices practice

Answer 1

1. Addition of matrices:

Given matrices A = [1 2] and B = [3 4], the sum of matrices A and B is calculated by adding corresponding elements:

A + B = [1+3 2+4] = [4 6]

2. Subtraction of matrices:

Given matrices C = [7 8] and D = [5 6], the difference between matrices C and D is calculated by subtracting corresponding elements:

C - D = [7-5 8-6] = [2 2]

3. Scalar multiplication of a matrix:

Given matrix E = [
1 2
3 4
] and scalar k = 2, the scalar multiplication of matrix E by k is calculated by multiplying every element of E by k:

k*E = [
2*1 2*2
2*3 2*4
] = [
2 4
6 8
]

4. Matrix multiplication:

Given matrices F = [2 3] and G = [
4 5
6 7
], the product of matrices F and G is calculated as follows:

F * G = [
2*4+3*6 2*5+3*7
] = [26 31]

5. Transpose of a matrix:

Given matrix H = [
1 2
3 4
], the transpose of matrix H is obtained by switching the rows and columns:

Transpose(H) = [
1 3
2 4
]