Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Show that a matrix which is both symmetric and skew symmetric is a zero matrix.

Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`

Let A = `[(2, 3),(-1, 2)]`. Then show that A² – 4A + 7I = O. Using this result calculate A⁵ also.

If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.

If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.

If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A² – B² 

Show that A′A and AA′ are both symmetric matrices for any matrix A.

If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A^–1 = A′, find value of α

If the matrix `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`, is a skew symmetric matrix, find the values of a, b and c.

If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.

Express the matrix `[(2, 3, 1),(1, -1, 2),(4, 1, 2)]` as the sum of a symmetric and a skew-symmetric matrix.

The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.

The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.

If A and B are matrices of same order, then (AB′ – BA′) is a ______.

______ matrix is both symmetric and skew-symmetric matrix.

Sum of two skew-symmetric matrices is always ______ matrix.

If A is a symmetric matrix, then A³ is a ______  matrix.

If A is a skew-symmetric matrix, then A² is a ______.

If A is skew-symmetric, then kA is a ______. (k is any scalar)

If A and B are symmetric matrices, then AB – BA is a ______.