matrices. examples:
TRANSCRIPT
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.