The number of solutions of the matrix equation is:

Question

Question

This question was previously asked in

AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper

Answer 1

Given:

Concept:

For the two matrices to be equal, each element of first matrix must be equal to the corresponding element in the second matrix.

Calculation:

Let

So,

Then

For the two matrices to be equal, each element of first matrix must be equal to the corresponding element in the second matrix. Therefore, we get

a² + bc =1...(i)

b(a + d) = 1...(ii)

c(a + d) = 2...(iii)

bc + d² = 3...(iv)

From equation (i) we have

From equation (iii) and (v), we get

⇒ (1 - a²)(a + d) = 2b

⇒ a + d - a³ - a²d = 2b

⇒ a³ + a²d - a + (2b - d) = 0 is an equation of third degree and it will have three solutions.

Therefore,

b, c

and

d

will also have three values corresponding to the values of

a

.

Therefore, the matrix equation has more than 2 solutions.

Hence the option (2) is correct.

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