Question

Choose the correct answer from the given alternatives in the following question:

If A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A^-1 = _____

पर्याय

• `[(1/("cos"alpha),-1/("sin" alpha)),(1/("sin"alpha),1/("cos"alpha))]`

• `[("cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`

• `[(-"cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`

• `[(-"cos"alpha,"sin"alpha),("sin"alpha, -"cos"alpha)]`

Answer 1

`[("cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`

Explanation:

A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`

|A| = cos²α + sin²α = 1

A⁻¹ = `1/|"A"| "Adj"("A") = 1/1 [("cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`