Question

If A = `[(1, 2, 3),(3, 2, 1)]`, B = `[(1, 0),(2, -1),(0, 2)]` and C = `[(0, 1),(-2, 5)]` Which of the following statements are correct?

(i) AB + C = `[(5, 5),(5, 5)]`

(ii) BC = `[(0, 1),(2, -3),(-4, 10)]`

(iii) BA + C = `[(2, 5),(3, 0)]`

(iv) (AB)C = `[(-8, 20),(-8, 13)]`

विकल्प

• (i) and (ii) only

• (ii) and (iii) only

• (iii) and (iv) only

• all of these

Answer 1

(i) and (ii) only

Explanation;

Hint:

(i) AB + C : order of A = 2 × 3

order of B = 3 × 2

order of AB = 2 × 2

order of C = 2 × 2

It is possible to add AB + C

(ii) BC :

order of B = 3 × 2

order of C = 2 × 2

It is possible to find BC

(iii) BA is not possible

order of B = 3 × 2

order of A = 3 × 2

BA does not exist.

BA + C is not a correct statement

(iv) ABC is not possible

order of A = 2 × 3 order of

B = 3 × 2

order of AB = 2 × 2

order of C = 3 × 2

It is not possible to multiply AB and C.

∴ The statement ABC is not correct.