Page 1 CBSE TEST PAPER-05 CLASS - XII MATHEMATICS (algebra) Topic:- Matrices 1. Show that 0 1 -1 -1 0 1 1 -1 0 A ? ? ? ? = ? ? ? ? ? ? , is skew symmetric matrix. [1] 2. 2 4 , 5 6 A ? ? = ? ? ? ? Prove that ' A A + is a symmetric matrix [1] 3. If -1 5 3 2 A ? ? = ? ? ? ? show that ( ) 3 ' 3 ' A A = [1] 4. Solve for x and y, given that y 1 3 3y x 2 5 x ? ?? ? ? ? = ? ?? ? ? ? ? ?? ? ? ? [1] 5. Given example of matrix A and B such that AB = 0 but A ? 0, B ? 0 [1] 6. If cos sin -sin cos A ? ? ? ? ? ? = ? ? ? ? then prove that cos n sin n -sin n cos n n A ? ? ? ? ? ? = ? ? ? ? [4] 7. Find X and Y, if 2x + 3y = 2 3 2 -2 3 2 4 0 -1 5 and x y ? ? ? ? + = ? ? ? ? ? ? ? ? [4] 8. If 2 2 2 2 cos sin cos sin cos cos = , = sin sin cos sin cos sin A B a a ß ß a ß a ß a a ß ß ? ? ? ? ? ? ? ? ? ? ? ? Show that AB is a zero matrix if a and ß differ by an odd multiple of . 2 p [4] 9. If f(x) = x 2 – 5x + 7 and 3 1 -1 2 A ? ? = ? ? ? ? find f(A) [4] 10. 4 3 , 2 5 A ? ? = ? ? ? ? find x and y such that A 2 – xA + yI = 0 [4]Read More

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