Mathematics - Vectors and Matrices
37. The system of simultaneous equations
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
has
- Option : C
- Explanation : Given equations are;
x + 2y + z = 6;
2x + y + 2z = 6;
x + y + z = 5
Given system can be written as
Applying row operation
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
39. Eigen values of the matrix
|
are |
,then eigen values of the matrix, I+A+A2 ,where I denotes the identity matrix are
- Option : C
- Explanation :
A + I is a triangular matrix. Since eigen values of a triangular matrix are is diagonal elements,
therefore eigen values of
are 3, 7, 13.
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