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RD Chapter 5 Algebra of Matrices Ex 5.3 Solutions

Question - 1 : -

Compute theindicated products:

Answer - 1 : -

(i) Consider

On simplification we get,

(ii) Consider

On simplification we get,

(iii) Consider

On simplification we get,

Question - 2 : -

Show that AB ≠ BAin each of the following cases:

Answer - 2 : -

(i) Consider,

Again consider,

From equation (1) and (2), it is clear that

AB ≠ BA

(ii) Consider,

Now again consider,

From equation (1) and (2), it is clear that

AB ≠ BA

(iii) Consider,

Now again consider,

From equation (1) and (2), it is clear that

AB ≠ BA

Question - 3 : -

Compute theproducts AB and BA whichever exists in each of the following cases:

Answer - 3 : -

(i) Consider,

BA does not exist

Because the number of columns in B is greater than the rows in A

(ii) Consider,

Again consider,

(iii) Consider,

AB = [0 + (-1) + 6 + 6]

AB = 11

Again consider,

(iv) Consider,

Question - 4 : -

Show that AB ≠ BAin each of the following cases:

Answer - 4 : -

(i) Consider,

Again consider,

From equation (1) and (2), it is clear that

AB ≠ BA

(ii) Consider,

Again consider,

From equation (1) and (2) it is clear that,

AB ≠ BA

Question - 5 : - Evaluate the following:

Answer - 5 : -

1.

2.

3.

Question - 6 : -

Answer - 6 : -


Question - 7 : -

Answer - 7 : -


Question - 8 : -

Answer - 8 : -


Question - 9 : -

Answer - 9 : -


Question - 10 : -

Answer - 10 : -


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