1
GATE CSE 2011
+2
-0.6
Four matrices $${M_1},\,\,\,{M_2},\,\,\,{M_3}$$ and $${M_4}$$ of dimensions $$p\,\,x\,\,q,\,\,\,\,\,q\,\,x\,\,e,\,\,\,\,\,r\,\,x\,\,s$$ and $$\,\,\,\,s\,\,x\,\,t$$ respectively can be multiplied in sevaral ways with different number of total scalar multiplications. For example when multiplied as $$\left( {\left( {{M_1}\,\,X\,\,{M_2}} \right)\,\,X\,\,\left( {{M_3}\,\,X\,\,{M_4}} \right)} \right)$$, the total number of scalar multiplications is $$\,\,\,\,$$$$pqr + rst + prt$$. When multiplied as $$\left( {\left( {\left( {{M_1}\,\,X\,\,{M_2}} \right)\,\,X\,\,{M_3}} \right)X\,\,{M_4}} \right)$$, the total number of scalar multiplications is $$pqr + prs + pst$$. If $$p = 10,\,\,q = 100,\,\,r = 20,\,\,s = 5,\,\,$$ and $$t = 80$$, then the minimum number of scalar multiplications needed is
A
$$248000$$
B
$$44000$$
C
$$19000$$
D
$$25000$$
2
GATE CSE 2011
+2
-0.6
Consider the matrix as given below. $$\left[ {\matrix{ 1 & 2 & 3 \cr 0 & 4 & 7 \cr 0 & 0 & 3 \cr } } \right]$$\$

Which of the following options provides the Correct values of the Eigen values of the matrix?

A
$$1, 4, 3$$
B
$$3, 7, 3$$
C
$$7, 3, 2$$
D
$$1, 2, 3$$
3
GATE CSE 2011
+2
-0.6
$$\left[ A \right]$$ is a square matrix which is neither symmetric nor skew-symmetric and $${\left[ A \right]^T}$$ is its transpose. The sum and differences of these matrices and defined as $$\left[ S \right] = \left[ A \right] + {\left[ A \right]^T}$$ and $$\left[ D \right] = \left[ A \right] - {\left[ A \right]^T}$$ respectively. Which of the following statements is true?
A
Both $$\left[ S \right]$$ and $$\left[ D \right]$$ are symmetric
B
Both $$\left[ S \right]$$ and $$\left[ D \right]$$ are skew-symmetric
C
$$\left[ S \right]$$ is skew-symmetric and $$\left[ D \right]$$ is symmetric
D
$$\left[ S \right]$$ is symmetric and $$\left[ D \right]$$ is skew symmetric
4
GATE CSE 2010
+2
-0.6
Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right]\,\,$$ If the eigen values of $$A$$ are $$4$$ and $$8$$, then
A
$$x = 4,\,\,y = 10$$
B
$$x = 5,\,\,y = 8$$
C
$$x = -3,\,\,y = 9$$
D
$$x = -4,\,\,y = 10$$
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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