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 = [a_{ij}]_{4x3}, B = [b_{ij}]_{3x2}

(ii)PQ, where P = [p_{ij}]_{4x3}, Q = [q_{ij}]_{4x3}

(iii)MN, where M = [m_{ij}]_{3x1}, N = [n_{ij}]_{1x5}

(iv) RS, where R = [r_{ij}]_{2x2}, S = [s_{ij}]_{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[a_{ij}]_{4 x 3} and B = [b_{ij}]_{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[p_{ij}]_{4 x 3} and Q = [q_{ij}]_{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[m_{ij}]_{3 x 1} and N = [n_{ij}]_{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[r_{ij}]_{2 x 2} and S = [s_{ij}]_{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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