Question

If A = `[(cos theta, sin theta, 0),(-sintheta, costheta, 0),(0, 0, 1)]`, where A₁₁, A₁₁, A₁₃ are co-factors of a₁₁, a₁₂, a₁₃ respectively, then the value of a₁₁A₁₁ + a₁₂A₁₂ + a₁₃A₁₃ = ______.

Options

• – 1

• 1

• 0

• `1/2`

Answer 1

If A = `[(cos theta, sin theta, 0),(-sintheta, costheta, 0),(0, 0, 1)]`, where A₁₁, A₁₁, A₁₃ are co-factors of a₁₁, a₁₂, a₁₃ respectively, then the value of a₁₁A₁₁ + a₁₂A₁₂ + a₁₃A₁₃ = 1.

Explanation:

 a₁₁A₁₁ + a₁₂A₁₂ + a₁₃A₁₃ 

= cosθ(cosθ – 0) + sinθ[–(–sinθ – 0)] + 0(0 – 0)

= cos²θ + sin²θ

= 1