Advertisements
Advertisements
प्रश्न
If A = `[(1, "a"),(0, 1)]`, then compute A4
उत्तर
A = `[(1, "a"),(0, 1)]`
A2 = A . A
= `[(1, "a"),(0, 1)] [(1, "a"),(0, 1)]`
= `[(1 + 0, "a" + "a"),(0 + 0, 0 + 1)]`
A2 = `[(1, 2"a"),(0, 1)]`
A4 = A2 × A2
= `[(1, "a"),(0, 1)] [(1, 2"a"),(0, 1)]`
A4 = `[(1 + 0, 2"a" + 2"a"),(0 + 0, 0 + 1)]`
A4 = `[(1, 4"a"),(0, 1)]`
APPEARS IN
संबंधित प्रश्न
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 elements a22, a23, a24, a34, a43, a44
If A = `[(5, 4, 3),(1, -7, 9),(3, 8, 2)]` then find the transpose of A
If A = `[(sqrt(7), - 3),(- sqrt(5), 2),(sqrt(3), -5)]` then find the transpose of – A
Find X and Y if X + Y = `[(7, 0),(3, 5)]` and X – Y = `[(3, 0),(0, 4)]`
Show that the matrices A = `[(1, 2),(3, 1)]`, B = `[(1, -2),(-3, 1)]` satisfy commutative property AB = BA
If A = `[(costheta, sintheta),(-sintheta, costheta)]` prove that AAT = I
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix AT is
If `cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta[(x, -cos theta),(cos theta, x)]` = I2, find x.
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 and BA ≠ 0
If A is a square matrix such that A2 = A, find the value of 7A – (I + A)3
Verify the property A(B + C) = AB + AC, when the matrices A, B, and C are given by A = `[(2, 0, -3),(1, 4, 5)]`, B = `[(3, 1),(-1, 0),(4, 2)]` and C = `[(4, 7),(2, 1),(1,-1)]`
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(A – B)T = AT – BT
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)]`
Choose the correct alternative:
If A and B are symmetric matrices of order n, where (A ≠ B), then
Choose the correct alternative:
If the points (x, – 2), (5, 2), (8, 8) are collinear, then x is equal to
Choose the correct alternative:
If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is
Let P = `[(3, -1, -2),(2, 0, alpha),(3, -5, 0)]`, where α ∈ R. Suppose Q = [qij] is a matrix satisfying PQ = kI3 for some non-zero k ∈ R. If q23 = `-k/8` and |Q| = `k^2/2`, then α2 + k2 is equal to ______.
Let A = `[(cosα, -sinα),(sinα, cosα)]`, α ∈ R such that A32 = `[(0, -1),(1, 0)]`. Then a value of α is ______.
If Aα = `[(cosα, sinα),(-sinα, cosα)]`, then which of following statement is TRUE?