If , write the value of a – 2b.
We are given that,
We need to find the value of a – 2b.
We know by the property of matrices,
This implies,
a11 = b11, a12 = b12, a21 = b21 and a22 = b22
Therefore,
a + 4 = 2a + 2 …(i)
3b = b + 2 …(ii)
8 = 8
-6 = a – 8b …(iii)
We have the equations (i), (ii) and (iii).
From equation (i),
a + 4 = 2a + 2
⇒ 2a – a = 4 – 2
⇒ a = 2
From equation (ii),
3b = b + 2
⇒ 3b – b = 2
⇒ 2b = 2
⇒ b = 1
We have a = 2 and b = 1.
Substituting the values of a and b in
a – 2b = 2 – 2(1)
⇒ a – 2b = 2 – 2
⇒ a – 2b = 0
Thus, the value of a – 2b is 0.