1
GATE CSE 2014 Set 3
+1
-0.3
Which one of the following statements is TRUE about every $$n\,\, \times \,n$$ matrix with only real eigen values?
A
If the trace of the matrix is positive and the determinant of the negative, at least one of its eigen values is negative.
B
If the trace of the matrix is positive, all its eigen values are positive.
C
If the determinanant of the matrix is positive, all its eigen values are positive.
D
If the product of the trace and determination of the matrix is positive, all its eigen values are positive.
2
GATE CSE 2014 Set 3
Numerical
+1
-0
If $${V_1}$$ and $${V_2}$$ are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of $${V_1}\, \cap \,\,{V_2}$$ is _________________.
3
GATE CSE 2014 Set 1
Numerical
+1
-0
The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4-by-4 symmetric positive definite matrix is ____________.
4
GATE CSE 2014 Set 1
Numerical
+1
-0
Consider the following system of equations:
3x + 2y = 1
4x + 7z = 1
x + y + z =3
x - 2y + 7z = 0
The number of solutions for this system is ______________________