Q. 15.0( 2 Votes )

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

order of the product.

(i) AB, where A = [aij]4x3, B = [bij]3x2

(ii)PQ, where P = [pij]4x3, Q = [qij]4x3

(iii)MN, where M = [mij]3x1, N = [nij]1x5

(iv) RS, where R = [rij]2x2, S = [sij]2x2

Answer :

(i) The multiplication of 2 matrices is possible if number of columns in first matrix is equal to number of rows in second.


Here A[aij]4 x 3 and B = [bij]3x2


Number of columns in A = 3


Number of rows in B = 3


Thus the product is defined and the order if product is


Number of rows in A × Number of columns in B


AB = 4 × 3


(ii) The multiplication of 2 matrices is possible if number of columns in first matrix is equal to number of rows in second.


Here P[pij]4 x 3 and Q = [qij]4x3


Number of columns in P = 3


Number of rows in Q = 4


Thus the product is not defined.


(iii) The multiplication of 2 matrices is possible if number of columns in first matrix is equal to number of rows in second.


Here M[mij]3 x 1 and N = [nij]1x5


Number of columns in M = 1


Number of rows in N = 1


Thus the product is defined and the order if product is


Number of rows in M × Number of columns in N


MN = 3 × 5


(iv) The multiplication of 2 matrices is possible if number of columns in first matrix is equal to number of rows in second.


Here R[rij]2 x 2 and S = [sij]2x2


Number of columns in R = 2


Number of rows in S = 2


Thus the product is defined and the order if product is


Number of rows in R × Number of columns in S


RS = 2 × 2


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