Question

1. Determine whether the product of the matrices is defined in each case. If so, state the order of the product.

Answer 1

Hi ,

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Multiplication Rule :

To multiply an m × n matrix by an n × p

matrix , the n's must be the same and the

result is an m × p matrix .

Or

The number of columns of 1st matrix must

equal the number of rows of the 2nd matrix.

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i ) Order of matrix A = 4 × 3

****** Order of matrix B = 3 × 2

here number of columns in A is equals to


number of rows in B

Order of AB = 4 × 2

ii ) Order of P = 4 × 3

Order of Q = 4 × 3

Here ,

number of columns in P is not equals to

number of rows in Q .

therefore ,

P × Q is not possible.

iii ) Order of M = 3 × 1

Order of N = 1 × 5

Here ,

number of columns in M is equals to number

of rows in N .

Order of MN = 3 × 5

iv ) Order of R = 2 × 2

Order of S = 2 × 2

Here,

number of columns in R is equals to number

of rows in S .

Order of RS = 2 × 2

I hope this helps you.

: )