Mathematics MCQ - Vectors and Matrices
Given equations are;
x + 2y + z = 6;
2x + y + 2z = 6;
x + y + z = 5
Given system can be written as
Applying row operation Â
we get,
we get,
Since rank of co-efficient matrix is 2 and rank of argument matrix is 3, which is not equal. Hence system has no solution.
The inverse of A is
= 5[3 - 0] - 0[0 - 2] + 2[0 - 6]
= 15 - 12
= 3
40
If      
Â
,then eigen values of the matrix, I+A+A2Â ,where I denotes the identity matrix are
A + I is a triangular matrix. Since eigen values of a triangular matrix are is diagonal elements,Â
therefore eigen values ofÂ
are 3, 7, 13.
