1
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.

The determinant of the resultant matrix is _________.

2
GATE CSE 2015 Set 3
+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?

A
$$p-q+r=0$$ or $$p=q=-r$$
B
$$p+q-r=0$$ or $$p=-q=r$$
C
$$p+q+r=0$$ or $$p=q=r$$
D
$$p-q+r=0$$ or $$p=-q=-r$$
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 ____ .
4
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
$$25000$$
GATE CSE Subjects
EXAM MAP
Medical
NEET