Advertisements
Advertisements
Question
If `cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta[(x, -cos theta),(cos theta, x)]` = I2, find x.
Solution
`[(cos theta, sin theta),(-sin theta, cos theta)] xx [(cos theta, - x),(x, cos theta)]` = I2
`[(cos^2theta + xsintheta, -xsintheta + sinthetacostheta),(-sinthetacostheta + xcostheta, xsintheta + cos^2theta)] = [(1, 0),(0, 1)]`
`[(cos^2theta + xsintheta, 0),(0, xsintheta + cos^2theta)] = [(1, 0),(0, 1)]`
cos2θ + x sinθ = 1
x sinθ = 1 – cos2θ
x sinθ = sin2θ
x = `(sin^2theta)/(sin theta)`
x = sinθ
– x cosθ + sinθ cosθ = 0
sinθ cosθ = x cosθ
⇒ sinθ = x ...(÷ cosθ)
∴ x = sinθ
The value of x = sinθ
APPEARS IN
RELATED QUESTIONS
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, write The order of the matrix
If A = `[(costheta, sintheta),(-sintheta, costheta)]` prove that AAT = I
If A is a 2 × 3 matrix and B is a 3 × 4 matrix, how many columns does AB have
If A = `[(1, 0, 0),(0, 1, 0),("a", "b", - 1)]`, show that A2 is a unit matrix
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(4, -2),(3, -5)]`
For what value of x, the matrix A = `[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)]` is skew – symmetric
If A and B are symmetric matrices of same order, prove that AB – BA is a skew-symmetric matrix
Choose the correct alternative:
If the square of the matrix `[(alpha, beta),(γ, - alpha)]` is the unit matrix of order 2, then α, β, and γ should
Choose the correct alternative:
If A + I = `[(3, -2),(4, 1)]`, then (A + I)(A – I) is equal to
