EXAMPLES ON MATRIX EQUALITY

Two matrices are equal if and only if the matrices have the same shape and elements in corresponding positions are equal.

Example 1 :

If

find p, q, r and s.

Solution :

Both are 2x 2 matrices, so they are equal and their corresponding terms will be equal.

By equating corresponding terms, we get

p  =  9

q+1  =  -2

q  =  -2-1

q  =  -3

r2  =  4

r  =  √4

r  =  ±2

5  =  s

s  =  5

So, the values of p, q, r and s are 9, -3, ±2 and 5 respectively.

Example 2 :

Solution :

By equating corresponding terms, we get

a  =  1, b  =  -5, c  =  2 and d  =  3.

Example 3 :

Solution :

By equating corresponding terms, we get

x  =  -2

a  =  5

2a  =  b

By applying the value of a in 2a  =  b, we get 

2(5)  =  b

b  =  10

So, the value of x is -2, a  =  5 and b  =  10.

Example 4 :

Solution :

By equating corresponding terms, we get

x  =  4

1-y  =  0

y  =  1

z  =  -2

So, the value of x is 4, y  =  1 and z  =  -2.

Example 5 :

Solution :

x2  =  9

x  =   ±3 

But equating x-1 to 2, we get

x  =  3

y  =  -y

y+y  =  0

2y  =  0

y  =  0

z  =  z

 z- z  =  0

z(z-1)  =  0

z  =  0 and z  =  1

So, the value of x is 3, y = 0 and z  =  0 or 1.

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