Operations On Matrices

1. Addition of matrices

For two matrices to be added, their order must be same. ie if a matrix A(m,n) and matrix B(y,z) to be added, then m should be equal to y and n should be equal to z.

To add the two matrices together, add their respective elements of same position. eg adding the following matrices:

The addition would look like : 

finally the resulting matrix would look like 

2. Multiplication of Matrix by a Scaler value

Given the following matrix contating the data of production of Item A and B, in two different shift of the day

Consider a factor that one day the production doubled its value. So the new matrix to be represented is as follows: 

Thus the final resulting matrix is represented by : 

Thus, if A = [aij] m × n is a matrix and k is a scalar quantity, then kXA is another matrix which is obtained by multiplying each element of A by the scalar k.

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