1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If the following system has non - trivial solution
$$$px+qy+rz=0$$$
$$$qx+ry+pz=0$$$
$$$rx+py+qz=0$$$
Then which one of the following Options is TRUE?
2
GATE CSE 2015 Set 2
Numerical
+2
-0
Perform the following operations on the matrix $$\left[ {\matrix{
3 & 4 & {45} \cr
7 & 9 & {105} \cr
{13} & 2 & {195} \cr
} } \right]$$
(i) Add the third row to the second row
(ii) Subtract the third column from the first column.
(i) Add the third row to the second row
(ii) Subtract the third column from the first column.
The determinant of the resultant matrix is _________.
Your input ____
3
GATE CSE 2014 Set 2
Numerical
+2
-0
The product of the non-zero eigenvalues of
the matrix $$\left[ {\matrix{ 1 & 0 & 0 & 0 & 1 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 1 & 0 & 0 & 0 & 1 \cr } } \right]$$ is ____ .
the matrix $$\left[ {\matrix{ 1 & 0 & 0 & 0 & 1 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 0 & 1 & 1 & 1 & 0 \cr 1 & 0 & 0 & 0 & 1 \cr } } \right]$$ is ____ .
Your input ____
4
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
Questions Asked from Linear Algebra (Marks 2)
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