|G(β)| = = 1Cofactors of A are:C11 = cos β C21 = sin α C31 = sin βC12 = 0 C22 = 1 C32 = 0C13 = sin β C23 = 0 C33 = cos βAdj G(β) = = So, adj G(β) = …… (i)Now, [G(β)] – 1 = And, G( – β) = = Hence, [G (β)] – 1 = G( – β)

Q. 16 B5.0( 2 Votes )

Let

Class 12th RD Sharma - Volume 1 7. Adjoint and Inverse of a Matrix

Answer :

|G(β)| = = 1

Cofactors of A are:

C₁₁ = cos β C₂₁ = sin α C₃₁ = sin β

C₁₂ = 0 C₂₂ = 1 C₃₂ = 0

C₁₃ = sin β C₂₃ = 0 C₃₃ = cos β

Adj G(β) =

So, adj G(β) = …… (i)

Now, [G(β)] ^{– 1} =

And, G( – β) =

Hence, [G (β)] ^{– 1} = G( – β)

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