For what value of x and y are the following matrices equal?

Question

Philoid · Accepted Answer

Given two matrices are equal .i.e, A = B.

We know that if two matrices are equal, then the elements of each matrices are also equal.

∴2x + 1 = x + 3

⇒ 2x – x = 3 – 1

⇒ x = 2 ……(1)

And 2y = y² + 2

⇒ y² – 2y + 2 = 0

⇒

⇒ (No real solutions) …… (2)

And y² – 5y = – 6

⇒ y² – 5y + 6 = 0

⇒ y² – 3y – 2y + 6 = 0

⇒ y(y – 3) – 2(y – 3) = 0

⇒ (y – 3)(y – 2) = 0

⇒ y = 3 or 2 …… (3)

∴ From the above equations we can say that A and B can’t be equal for any value of y.