Question

Matrix P has x rows and x + 3 columns. Matrix Q has y rows and 7 – y
columns. If PQ and QP both are defined, find the orders of P and Q.

Answer 1

PQ and QP can be defined. So,addition of rows and columns of P and Q should be equal.

So,x+x+3=y+7-y

2x+3=7

2x=4

x=2

For multiplication of PQ columns of P=rows of Q.

So, x+3=y

2+3=5

5=5

x is equal to 2

y is equal to 5

order of P=2×5

order of Q=5×2

by the values of x and y.

we can define PQ and QP.

because coloumns in P is equal to rows inQ so multiplication of PQ can be defined and columns in Q is equal to rows in P so multiplication of QP can be defined.

The matrix formed by multipling P and Q is rows of P×columns of Q and the matrix formed by multipling Q and P is rows of Q×columns of P.

Hope it helps you.

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