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

(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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