Question

If A = `[(1,0,0),(2,"cos x","sin x"),(3,"sin x", "-cos x")],` then det. A is equal to ____________.

विकल्प

• sin2x

• 1

• cos2x

• -1

Answer 1

If A = `[(1,0,0),(2,"cos x","sin x"),(3,"sin x", "-cos x")],` then det. A is equal to -1.

Explanation:

`"det" ("A") = abs ((1,0,0),(2,"cos" theta, "sin" theta),(3, "sin" theta, "-cos" theta))`

Expanding along R₁

`1 ("- cos"^2 theta - "sin"^2 theta) - 1 ("cos"^2 theta + "sin"^2 theta)`