Advertisements
Advertisements
प्रश्न
If A = `[(costheta, theta),(0, costheta)]`, B = `[(sintheta, 0),(0, sintheta)]` then show that A2 + B2 = I
उत्तर
L.H.S. = A2 + B2
A2 = `[(costheta, 0),(0, costheta)][(costheta, 0),(0, costheta)]`
= `[(cos^2theta, 0),(0, cos^2theta)]`
B2 = `[(sintheta, 0),(0, sintheta)] [(sintheta, 0),(0, sintheta)]`
= `[(sin^2theta, 0),(0, sin^2theta)]`
A2 + B2 = `[(cos^2theta, 0),(0, cos^2theta)] + [(sin^2theta, 0),(0, sin^2theta)]`
= `[(sin^2theta + cos^2theta, 0),(0, sin^2theta + cos^2theta)]`
= `[(1, 0),(0, 1)]`
= I
= R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Construct a 3 × 3 matrix whose elements are given by aij = |i – 2j|
Find x and y if `x[(4),(-3)] + y[(-2),(3)] = [(4),(6)]`
If A is of order p × q and B is of order q × r what is the order of AB and BA?
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that A(BC) = (AB)C
If A = `[(1, 2, 3),(3, 2, 1)]`, B = `[(1, 0),(2, -1),(0, 2)]` and C = `[(0, 1),(-2, 5)]` Which of the following statements are correct?
(i) AB + C = `[(5, 5),(5, 5)]`
(ii) BC = `[(0, 1),(2, -3),(-4, 10)]`
(iii) BA + C = `[(2, 5),(3, 0)]`
(iv) (AB)C = `[(-8, 20),(-8, 13)]`
Consider the matrix Aα = `[(cos alpha, - sin alpha),(sin alpha, cos alpha)]` Show that `"A"_alpha "A"_beta = "A"_((alpha + beta))`
Find the matrix A which satisfies the matrix relation `"A"= [(1, 2, 3),(4, 5, 6)] = [(-7, -8, -9),(2, 4, 6)]`
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(BT)T = B
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`
Let A = `((1, -1, 0),(0, 1, -1),(0, 0, 1))` and B = 7A20 – 20A7 + 2I, where I is an identity matrix of order 3 × 3. If B = [bij], then b13 is equal to ______.
