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1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
In the given matrix $$\left[ {\matrix{ 1 & { - 1} & 2 \cr 0 & 1 & 0 \cr 1 & 2 & 1 \cr } } \right],$$ one of the eigenvalues is $$1.$$ The eigen vectors corresponding to the eigen value $$1$$ are
A
$$\left\{ {\alpha \left( {4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
B
$$\left\{ {\alpha \left( { - 4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
C
$$\left\{ {\alpha \left( {\sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
D
$$\left\{ {\alpha \left( { - \sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
2
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 ____________.
Your input ____
3
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 ______________________
Your input ____
4
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+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.
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Discrete Mathematics
Mathematical Logic Probability Set Theory & Algebra Combinatorics Linear Algebra Graph Theory Calculus
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Basic of Programming Language Function and Recursion Pointer and Structure in C
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