Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Show that the matrix  A = `[(1,-1,5),(-1,2,1),(5,1,3)]` is a symmetric matrix.

Show that the matrix  A = `[(0,1,-1),(-1,0,1),(1,-1,0)]` is a skew symmetric matrix.

For the matrix A = `[(1,5),(6,7)]` verify that (A + A') is a symmetric matrix.

For the matrix A = `[(1,5),(6,7)]` verify that (A - A') is a skew symmetric matrix.

Find `1/2` (A + A')  and  `1/2` (A -A') When `A = [(0, a, b),(-a,0,c),(-b,-c,0)]`

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

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

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

`[(6, -2,2),(-2,3,-1),(2,-1,3)]`

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

`[(3,3,-1),(-2,-2,1),(-4,-5,2)]`

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

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

If A and B are symmetric matrices, prove that AB − BA is a skew symmetric matrix.

Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Find the values of x, y, z if the matrix `A = [(0,2y,z),(x,y,-z),(x , -y,z)]` satisfy the equation A'A = I.

If the matrix A is both symmetric and skew symmetric, then ______.

Show that all the diagonal elements of a skew symmetric matrix are zero.

If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.

For what value of x, is the matrix \[A = \begin{bmatrix}0 & 1 & - 2 \\ - 1 & 0 & 3 \\ x & - 3 & 0\end{bmatrix}\] a skew-symmetric matrix?

If a matrix A is both symmetric and skew-symmetric, then

The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is