If , find the value of x.

We are given with,

We need to find the value of x.

By property of matrices,

Similarly,

…(i)

And,

…(ii)

Adding equations (i) and (ii),

Now,

Since

Adding the two matrices on the right hand side by simply adding the corresponding elements,

We know by the property of matrices,

This implies,

a₁₁ = b₁₁, a₁₂ = b₁₂, a₂₁ = b₂₁ and a₂₂ = b₂₂

So, this means that we can get two equations,

10 = 2x – y …(iii)

5 = 3x + y …(iv)

We have two equations and two variables.

Solving equations (iii) and (iv),

⇒ 5x = 15

⇒ x = 3

Thus, we get x = 3.