Question
Download Solution PDFIf
(where) I is the identity matrix.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF)Concept:
Expansion of determinant
Δ = a11 a22 a33 - a11 a23 a32 - a12 a21 a33 + a12 a23 a31 + a13 a21 a32 - a13 a31 a22
A(adj A) = ∣ A ∣ I, where I is the identity matrix.
Calculation:
Given:
⇒
Expanding about C3, we get,
⇒ ∣ A ∣ = 1{(2 sinθ × sinθ) + 2 cos2θ}
⇒ ∣ A ∣ = 1(2 sin2θ + 2 cos2 θ)
⇒ ∣ A ∣ = 2(sin2θ + cos2θ)
⇒ ∣ A ∣ = 2 [∵ sin2θ + cos2θ = 1]
⇒ A(adj A) = ∣ A ∣ I
Putting the value of ∣ A ∣ = 2,
⇒ A(adj A) = 2I, where I is the identity matrix.
∴ A(adj A) = 2I
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