1
GATE ECE 2014 Set 3
+1
-0.3
Which one of the following statements is NOT true for a square matrix $$A$$?
A
If $$A$$ is upper triangular, the eigenvalues of $$A$$ are the diagonal elements of it
B
If $$A$$ is real symmetric, the eigenvalues of $$A$$ are always real and positive
C
If $$A$$ is real , the eigenvalues of $$A$$ and $${A^T}$$ are always the same
D
If all the principal minors of $$A$$ are positive , all the eigenvalues of $$A$$ are also positive
2
GATE ECE 2014 Set 2
+1
-0.3
The system of linear equations $$\left( {\matrix{ 2 & 1 & 3 \cr 3 & 0 & 1 \cr 1 & 2 & 5 \cr } } \right)\left( {\matrix{ a \cr b \cr c \cr } } \right) = \left( {\matrix{ 5 \cr { - 4} \cr {14} \cr } } \right)$$ has
A
a unique solution
B
infinitely many solutions
C
no solution
D
exactly two solutions
3
GATE ECE 2014 Set 2
Numerical
+1
-0
The determinant of matrix $$A$$ is $$5$$ and the determinant of matrix $$B$$ is $$40.$$ The determinant of matrix $$AB$$ is _______.
4
GATE ECE 2014 Set 2
Numerical
+1
-0
The maximum value of the determinant among all $$2 \times 2$$ real symmetric matrices with trace $$14$$ is ______.
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