Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (A′)′ = (AB)' = B'A'

If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (kA)' = (kA')

If `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`, then find values of x, y, z and w.

If A = `[(1, 5),(7, 12)]` and B  `[(9, 1),(7, 8)]`, find a matrix C such that 3A + 5B + 2C is a null matrix.

Find the values of a, b, c and d, if `3[("a", "b"),("c", "d")] = [("a", 6),(-1, 2"d")] + [(4, "a" + "b"),("c" + "d", 3)]`

Find the matrix A such that `[(2, -1),(1, 0),(-3, 4)] "A" = [(-1, -8, -10),(1, -2, -5),(9, 22, 15)]`

If P(x) = `[(cosx, sinx),(-sinx, cosx)]`, then show that P(x) . (y) = P(x + y) = P(y) . P(x)

Find x, y, z if A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfies A′ = A^–1.

If possible, using elementary row transformations, find the inverse of the following matrices

`[(2, -1, 3),(-5, 3, 1),(-3, 2, 3)]`

If possible, using elementary row transformations, find the inverse of the following matrices

`[(2, 3, -3),(-1, 2, 2),(1, 1, -1)]`

If possible, using elementary row transformations, find the inverse of the following matrices

`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`

If `[(2x + y, 4x),(5x - 7, 4x)] = [(7, 7y - 13),(y, x + 6)]`, then the value of x + y is ______.

If A = `1/pi [(sin^-1(xpi), tan^-1(x/pi)),(sin^-1(x/pi), cot^-1(pix))]`, B = `1/pi [(-cos^-1(x/pi), tan^-1 (x/pi)),(sin^-1(x/pi),-tan^-1(pix))]`, then A – B is equal to ______.

On using elementary column operations C₂ → C₂ – 2C₁ in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: ______.

On using elementary row operation R₁ → R₁ – 3R₂ in the following matrix equation: `[(4, 2),(3, 3)] = [(1, 2),(0, 3)] [(2, 0),(1, 1)]`, we have: ______.

In applying one or more row operations while finding A^–1 by elementary row operations, we obtain all zeros in one or more, then A^–1 ______.

A matrix denotes a number.

Two matrices are equal if they have same number of rows and same number of columns.

If (AB)′ = B′ A′, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.