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# CBSE Test Paper (Algebra) (Class - XII Mathematics) Class 12 Notes | EduRev

## Class 12 : CBSE Test Paper (Algebra) (Class - XII Mathematics) Class 12 Notes | EduRev

``` Page 1

CBSE TEST PAPER-04
CLASS - XII MATHEMATICS (algebra)
Topic:- Matrices
1. If A and B are symmetric matrices of the same order, prove that AB + BA is symmetric [1]
2. If
2  3
,
4  5
A
? ?
=
? ?
? ?
Prove that A – A
t
is a skew – symmetric matrix [1]
3. If A is any square matrix, prove that AA
1
is symmetric [1]
4. Solve for x and y given that
2     -3 1
1  1 4 3
x ? ?? ? ? ?
=
? ?? ? ? ?
? ?? ? ? ?
[1]
5. Give example of matrices such that AB = 0, BA = 0, A ? 0,  B ? 0 [1]
6. Construct 2× 3 matrix whose element aij are given by [4]
2i+j     when     i<j
4i.j      when     i=j
i+2j     when     i>j
aij
? ?
? ?
=
? ?
? ?
? ?
7. If
1  2  3
3    -2     1 ,
4  2  1
A
? ?
? ?
=
? ?
? ?
? ?
then show that A
3
– 23A – 40I = 0 [4]
8. Express the matrix
2    -2    -4
-1    3     4
1    -2    -3
B
? ?
? ?
=
? ?
? ?
? ?
as the sum of a symmetric and a skew symmetric
matrix. [4]
9. If
n-1 n-1 n-1
n n-1 n-1 n-1
n-1 n-1 n-1
3 3 3
1  1  1
1    1    1 , that A = 3 3 3
1  1  1
3 3 3
A prove
? ?
? ?
? ?
? ?
=
? ?
? ?
? ?
? ?
? ?
? ?
[4]
10. If
8  0 2      -2
4    -2 4  2
3  6 -5     1
A B
? ? ? ?
? ? ? ?
= =
? ? ? ?
? ? ? ?
? ? ? ?
then find the matrix X such that 2A + 3X = 5B. [4]
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