PROBLEMS ON EQUALITY OF MATRICES

Here we are going to see some practice questions based on the concept of equality of matrices.

Question 1 :

Find the values of p, q, r, and s if As the orders of the two matrices are same, they are equal if and only if the corresponding entries are equal. Thus, by comparing the corresponding elements, we get

 Calculating value of p :p2 - 1  =  1p2  =  2p  =  ±√2 Calculating value of q :-3 - q3  =  -4- q3  =  -4 + 3- q3  =  -1  ==>  q  =  1 Calculating value of r :r + 1  =  3/2r  =  (3/2) - 1r  =  1/2 Calculating value of s :s - 1  =  -π s  = -π + 1

Question 2 :

Determine the value of x + y if Solution :

As the orders of the two matrices are same, they are equal if and only if the corresponding entries are equal. Thus, by comparing the corresponding elements, we get

2x + y  =  7  ---(1)

4x  =  7y - 13 ---(2)

5x  - 7  =  y   ---(3)

4x  =  x + 6

4x - x  =  6

3x  =  6

x  =  2

By applying the value of x in the first equation, we get

2(2) + y  =  7

4 + y  =  7

y  =  7 - 4  =  3

Hence the value of x + y is 5.

Note : By solving above equation, we will get the same answer.

Question 3 :

Determine the matrices A and B if they satisfy Solution : In order to eliminate A, let us multiply the second equation by 2 and subtract from the first equation.

(1) - 2 ⋅ (2)

L.H.S :

=  2A - B - 2(A - 2B)

=  2A - B - 2A + 4B

=  3B

R.H.S : In order to eliminate B, let us multiply the first equation by 2 and subtract second equation.

(1)  2 - (2)

L.H.S :

=  2(2A - B) - (A - 2B)

=  4A - 2B - A + 2B

=  3A

R.H.S : Hence the required matrices are  After having gone through the stuff given above, we hope that the students would have understood "Problems on Equality of Matrices".

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