Science (English Medium) Class 12 - CBSE Question Bank Solutions

If `A = [(-1,2,3),(5,7,9),(-2,1,1)]  "and"  B = [(-4,1,-5),(1,2,0),(1,3,1)]` then verify that (A+ B)' = A' + B'

if `A = [(-1,2,3),(5,7,9),(-2,1,1)] and B = [(-4,1,-5),(1,2,0),(1,3,1)]` then verify that (A- B)' = A' - B'

if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A + B)' = A' + B'

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

if A' = `[(-2,3),(1,2)] and B = [(-1,0),(1,2)]`  then find (A + 2B)'

For the matrices A and B, verify that (AB)′ = B'A' where `A =[(1),(-4), (3)], B = [-1, 2  1]`

For the matrices A and B, verify that (AB)′ = B'A'  where `A =[(0), (1),(2)] , B =[1 , 5, 7]`

If A = `[(cos alpha, sin alpha), (-sin alpha, cos alpha)]` then verify that  A' A = I

If A = `[(sin alpha, cos alpha), (-cos alpha, sin alpha)]` then verify that  A'A = I

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.