1
GATE CSE 2011
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
3
GATE CSE 2010
MCQ (Single Correct Answer)
+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
$$x = -4,\,\,y = 10$$
4
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
How many of the following matrices have an eigen value $$1$$?
$$\left[ {\matrix{ 1 & 0 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 0 & 1 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 1 & { - 1} \cr 1 & 1 \cr } } \right]\,\,and\,\,\left[ {\matrix{ { - 1} & 0 \cr 1 & { - 1} \cr } } \right]$$
A
one
B
two
C
three
D
four
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