MATRICES

EXAMPLES:

SOLUTION OF SYSTEM OF LINEAR EQUATION

ASSIGNMENT INVERSE OF EVERY SQUARE MATRIX IF IT EXIST IS UNIQUE? IF A AND B BE TWO NON SINGULAR MATRICES OF THE SAME ORDER n,THEN (AB) -1 =B -1 A -1 ? PROVE THAT ADJOINT OF A NON SINGULAR MATRIX IS NON SINGULAR.

SOLVE THE SYSTEM OF EQUATIONS USING MATRIX METHOD: 3x+y+2z=3 2x-3y-z=-3 x+2y+z=4 PROVE THAT THE DIAGONAL ELEMENTS OF THE SKEW SYMMETRIC MATRIX ARE ALL ZERO.

PROVE THAT EVERY SKEW SYMMETRIC MATRIX OF ODD ORDER IS THE SINGULAR MATRIX. EVERY SQUARE MATRIX A CAN BE EXPRESSED IN ONE AND ONLY ONE WAY AS P+iQ,WHERE P AND Q ARE HERMITION MATRIX.

TEST ATTEMPT ANY THREE: Q1. IF A AND B ARE SYMMETRIC MATRIX,SHOW THAT AB+BAIS SYMMETRIC AND AB-BA IS SKEW SYMMETRIC. Q2. IF A AND B ARE SKEW SYMMETRIC THEN A+B IS ALSO SKEW SYMMETRIC.

Q3. SHOW THAT ALL THE ELEMENTS ON THE MAIN DIAGONAL OF A SKEW SYMMETRIC MATRIX ARE ALL ZERO. Q4. SHOW THAT ALL THE POSITIVE INTEGRAL POWER OF A SYMMETRIC MATRIX ARE SYMMETRIC.