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Chapter 3 Matrices Ex 3.2 Solutions

Question - 1 : - Let 

Answer - 1 : -

Find each of thefollowing

(i)  (ii)  (iii) (iv)  (v) 

Solution

(i)

(ii)

(iii)

(iv) Matrix A has 2 columns.This number is equal to the number of rows in matrix B.Therefore, AB is defined as:

(v) Matrix B has 2 columns.This number is equal to the number of rows in matrix A.Therefore, BA is defined as:

Question - 2 : -

Compute the following:

Answer - 2 : -

(i)  (ii) 

(iii) 

(v) 

Solution

(i)

(ii) 

(iii) 

(iv) 


Question - 3 : -

Compute the indicatedproducts

Answer - 3 : -

(i)                               (ii) 

(iii)                 (iv) 

(v)                     (vi) 


Solution

(i) 


(ii) 

(iii) 


(iv) 


(v) 


(vi) 

Question - 4 : - If, and, then compute and. Also, verify that 

Answer - 4 : -

Question - 5 : - If andthen compute

Answer - 5 : -

Question - 6 : - Simplify 

Answer - 6 : -

Question - 7 : -

Find X and Y,if

Answer - 7 : -

(i) and

(ii) and 


Solution

(i)

Adding equations (1) and(2), we get:

(ii)

Multiplying equation (3)with (2), we get:

Multiplying equation (4)with (3), we get:

From (5) and (6), wehave:

Now,

Question - 8 : -

Find X,if and 

Answer - 8 : - We have

Question - 9 : -

Find x and y,if

Answer - 9 : - We have

Comparing thecorresponding elements of these two matrices, we have:

∴x = 3 and y = 3

Question - 10 : -

Solve the equationfor x, y, z and t if

Answer - 10 : - We have

Comparing thecorresponding elements of these two matrices, we get:

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