1
GATE ECE 2015 Set 1
Numerical
+1
-0
The value of $$'P'$$ such that the vector $$\left[ {\matrix{ 1 \cr 2 \cr 3 \cr } } \right]$$ is an eigenvector of the matrix $$\left[ {\matrix{ 4 & 1 & 2 \cr P & 2 & 1 \cr {14} & { - 4} & {10} \cr } } \right]$$ is ________.
2
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
3
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
4
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 _______.