1
GATE CE 2000
+1
-0.3
Consider the following two statements.

$$(I)$$ The maximum number of linearly independent column vectors of a matrix $$A$$ is called the rank of $$A.$$

$$(II)$$ If $$A$$ is $$nxn$$ square matrix then it will be non-singular if rank of $$A=n$$

A
Both the statements are false
B
Both the statements are true
C
$$(I)$$ is true but $$(II)$$ is false
D
$$(I)$$ is false but $$(II)$$ is true
2
GATE CE 2000
+1
-0.3
If $$A,B,C$$ are square matrices of the same order then $${\left( {ABC} \right)^{ - 1}}$$ is equal be
A
$${C^{ - 1}}\,{A^{ - 1}}\,{B^{ - 1}}$$
B
$${C^{ - 1}}\,{B^{ - 1}}\,{A^{ - 1}}$$
C
$${A^{ - 1}}\,{B^{ - 1}}\,{C^{ - 1}}$$
D
$${A^{ - 1}}\,{C^{ - 1}}\,{B^{ - 1}}$$
3
GATE CE 1999
+1
-0.3
If $$A$$ is any $$nxn$$ matrix and $$k$$ is a scalar then $$\left| {kA} \right| = \alpha \left| A \right|$$ where $$\alpha$$ is
A
$$kn$$
B
$${n^k}$$
C
$${k^n}$$
D
$${k \over n}$$
4
GATE CE 1999
+1
-0.3
The equation $$\left[ {\matrix{ 2 & 1 & 1 \cr 1 & 1 & { - 1} \cr y & {{x^2}} & x \cr } } \right] = 0$$ represents a parabola passing through the points.
A
$$(0, 1), (0, 2), (0, -1)$$
B
$$(0, 0), (-1, 1), (1, 2)$$
C
$$(1, 1), (0, 0), (2, 2)$$
D
$$(1, 2), (2, 1), (0, 0)$$
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