Commerce (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 ______.

Differentiate the function with respect to x. 

cos x . cos 2x . cos 3x

Differentiate the function with respect to x.

`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`

Differentiate the function with respect to x.

(log x)^{cos x}

Differentiate the function with respect to x.

x^x − 2^{sin x}

Differentiate the function with respect to x.

(x + 3)² . (x + 4)³ . (x + 5)⁴

Differentiate the function with respect to x.

`(x + 1/x)^x + x^((1+1/x))`

Differentiate the function with respect to x.

(log x)^x + x^{log x}