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1
GATE CE 2023 Set 1
MCQ (More than One Correct Answer)
+2
-0

For the matrix

$[A]= \begin{bmatrix}1&2&3\\\ 3&2&1\\\ 3&1&2 \end{bmatrix} $

which of the following statements is/are TRUE?

A
The eigenvalues of [A]T are same as the eigenvalues of [A] 
B
The eigenvalues of [A]-1 are the reciprocals of the eigenvalues of [A]
C
The eigenvectors of [A]T are same as the eigenvectors of [A] 
D
The eigenvectors of [A]-1 are same as the eigenvectors of [A]
2
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the matrix $$\left[ {\matrix{ 5 & { - 1} \cr 4 & 1 \cr } } \right].$$ Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?
A
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and only one independent eigenvector exists.
B
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and two independent eigen vectors exist.
C
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and no independent eigen vector exists
D
Eigenvalues are $$3$$ and $$-3,$$ and two independent eigenvectors exist
3
GATE CE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
If $$A = \left[ {\matrix{ 1 & 5 \cr 6 & 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 & 7 \cr 8 & 4 \cr } } \right]A{B^T}$$ is equal to
A
$$\left[ {\matrix{ {38} & {28} \cr {32} & {56} \cr } } \right]$$
B
$$\left[ {\matrix{ 3 & {40} \cr {42} & 8 \cr } } \right]$$
C
$$\left[ {\matrix{ {43} & {27} \cr {34} & {50} \cr } } \right]$$
D
$$\left[ {\matrix{ {38} & {32} \cr {28} & {56} \cr } } \right]$$
4
GATE CE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider the following linear system $$$x+2y-3z=a$$$ $$$2x+3y+3z=b$$$ $$$5x+9y-6z=c$$$
This system is consistent if $$a,b$$ and $$c$$ satisfy the equation
A
$$7a - b - c = 0$$
B
$$3a + b - c = 0$$
C
$$3a - b + c = 0$$
D
$$7a - b + c = 0$$
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