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]Read More

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