MATRICESMATRICES

EXAMPLES:EXAMPLES:

SOLUTION OF SYSTEM OF SOLUTION OF SYSTEM OF LINEAR EQUATIONLINEAR EQUATION

ASSIGNMENTASSIGNMENT

• 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-1A-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.

TESTTEST

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.