1
GATE CE 2017 Set 2
+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
$$\left[ {\matrix{ {38} & {32} \cr {28} & {56} \cr } } \right]$$
2
GATE CE 2017 Set 1
+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 2016 Set 2
+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
$$7a - b + c = 0$$
4
GATE CE 2015 Set 2
+2
-0.6
The two Eigen Values of the matrix $$\left[ {\matrix{ 2 & 1 \cr 1 & p \cr } } \right]$$ have a ratio of $$3:1$$ for $$p=2.$$ What is another value of $$'p'$$ for which the Eigen values have the same ratio of $$3:1$$?
A
$$-2$$
B
$$1$$
C
$$7/3$$
D
$$14/3$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Environmental Engineering
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Medical
NEET