1
GATE CSE 2004
+1
-0.3
Let A, B, C, D be $$n\,\, \times \,\,n$$ matrices, each with non-zero determination. If ABCD = I, then $${B^{ - 1}}$$ is
A
$${D^{ - 1}}\,\,\,{C^{ - 1}}\,\,{A^{ - 1}}$$
B
CDA
C
D
Does not necessarily exist
2
GATE CSE 2004
+1
-0.3
What values of x, y and z satisfy the following system of linear equations? $$\left[ {\matrix{ 1 & 2 & 3 \cr 1 & 3 & 4 \cr 2 & 3 & 3 \cr } } \right]\,\,\left[ {\matrix{ x \cr y \cr z \cr } } \right]\,\, = \,\left[ {\matrix{ 6 \cr 8 \cr {12} \cr } } \right]$$\$
A
x = 6, y = 3, z = 2
B
x = 12, y = 3, z = - 4
C
x = 6, y = 6, z = - 4
D
x = 12, y = - 3, z = 0
3
GATE CSE 2004
+1
-0.3
The number of different $$n \times n$$ symmetric matrices with each elements being either $$0$$ or $$1$$ is
A
$${2^n}$$
B
$${2^{{n^2}}}$$
C
$${2^{{{{n^2} + n} \over 2}}}$$
D
$${2^{{{{n^2} - n} \over 2}}}$$
4
GATE CSE 2003
+1
-0.3
$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix containing coefficients has a non-trival solution when $$A$$ is.
A
non-singular
B
singular
C
symmetric
D
Hermitian
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
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