Mrs. JAYA.S PGT (MATHS)
28 June 2011
MATRICES
1. Find x,
2.If A= then prove by M.I that
3.A = 
, find f(A) , where f(x) =
4.Find K such that ,if A= satisfies the equation
5.If A= B = Express 3A + 2B as the sum of symmetric and skew symmetric matrices.
DETERMINANTS
1.If A is a 3 x 3 matrix , =12, Find
2.If A is a 3 x3 matrix =-4 .Find
3.Find , =3 and A is a 4 x4 matrix.
4.For what values of k, A = is not invertible.
5.Show that the points ( a, b+c ) ; (b, c+a) ; ( c, a+b ) are collinear using determinants.
6. Find the equation of the line joining (1,2) ; (3,6) using determinants.
7. If the area of triangle is 35 sq. units with vertices (2,-6) ; (5,4) ; (k,4) . Find the value of k
using determinants.
8. IfA= Find A. adj A , without finding adjA.
10. Show that the matrix, A=satisfies the equation. Hence find.
11.Using properties of determinants, prove that=+
1 2. Using properties of determinants, prove =
13. Solve the equation, =0 14. Using properties of determinants, prove that =ab+bc+ca+abc
15. Using properties of determinants, prove that
=1+ +
16. If x,y,z are different and =0 , then show that 1+xyz=0.
18.Using properties of determinants, Solve the equation, if.=0
19.Show that A. adj A =. where A =
20.Find the inverse of A, If A= .
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