1
GATE CSE 1997
+2
-0.6
Let $$A = ({a_{ij}})$$ be and n-rowed square matrix and $${I_{12}}$$ be the matrix obtained by interchanging the first and second rows of the n-rowed Identity matrix. Then$${AI_{12}}$$ is such that its first
A
row is the same as its second row
B
row is the same as the second row of A
C
column is the same as the second column A
D
row is all zero
2
GATE CSE 1996
+2
-0.6
The matrices$$\left[ {\matrix{ {\cos \,\theta } & { - \sin \,\theta } \cr {\sin \,\,\theta } & {\cos \,\,\theta } \cr } } \right]\,\,and$$
$$\left[ {\matrix{ a & 0 \cr 0 & b \cr } } \right]\,$$ commute under multiplication
A
if a = b or $$\theta = n\,\pi$$, n an integer
B
always
C
never
D
if a cos $$\theta \,\, \ne \,\,b\,\,\sin \,\theta$$
3
GATE CSE 1994
+2
-0.6
If A and B are real symmetric matrices of size n x n. Then, which one of the following is true?
A
$$A{A^t} = I$$
B
$$A = A - 1$$
C
AB = BA
D
$${(AB)^T} = {B^T}{A^T}$$
4
GATE CSE 1994
+2
-0.6
In a compact single dimensional array representation for lower triangular matrices (i.e., all the elements above the diagonal are zero) of size $$n$$ $$x$$ $$n$$, non-zero elements (i.e., elements of the lower triangle) of each row are stored one after another, starting from the first row, the index of the $${\left( {i,\,j} \right)^{th}}$$ element of the lower triangular matrix in this new representation is
A
$${i+\,j}$$
B
$${i + j - 1}$$
C
$$j + {{i\left( {i - 1} \right)} \over 2}$$
D
$$i + {{j\left( {j - 1} \right)} \over 2}$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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