Find the product of the matrices, if exists,

(i) (ii)

(iii) (iv)

(i) ⇒ let A : [2 -1] ∴ A[a_ij]_{1 × 2}

⇒ let B : ∴ B[b_ij]_{2 × 1}

Number of columns in A = 2

Number of rows in B = 2

Thus the product is defined and the order if product is

Number of rows in A × Number of columns in B

∴ AB = 1 × 1

⇒ [2 × 5 + (-1) × 4]

⇒ [10-4]

⇒ [6]

(ii) ⇒ let A : ∴ A[a_ij]_{2 × 2}

⇒ let B : ∴ B[b_ij]_{2 × 2}

Number of columns in A = 2

Number of rows in B = 2

Thus the product is defined and the order if product is

Number of rows in A × Number of columns in B

∴ AB = 2 × 2

⇒

⇒

(iii) ⇒ let A : ∴ A[a_ij]_{2 × 3}

⇒ let B : ∴ B[b_ij]_{3 × 2}

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 = 2 × 2

⇒

⇒

(iv) let A : ∴ A[a_ij]_{2 × 1}

let B : [2 7] ∴ B[b_ij]_{1 × 2}

Number of columns in A = 1

Number of rows in B = 1

Thus the product is defined and the order if product is

Number of rows in A × Number of columns in B

∴ AB = 2 × 2

× [2 -7]

⇒

⇒