1
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 $$p=-q=-r$$ 2 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 ____ . Your input ____ 3 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 $$25000$$ 4 GATE CSE 2011 MCQ (Single Correct Answer) +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
$$1, 2, 3$$
GATE CSE Subjects
EXAM MAP
Medical
NEET