1
GATE CE 2016 Set 2
+2
-0.6
Consider the following linear system $$x+2y-3z=a$$$$$2x+3y+3z=b$$$ $$5x+9y-6z=c$$\$
This system is consistent if $$a,b$$ and $$c$$ satisfy the equation
A
$$7a - b - c = 0$$
B
$$3a + b - c = 0$$
C
$$3a - b + c = 0$$
D
$$7a - b + c = 0$$
2
GATE CE 2015 Set 1
+2
-0.6
The smallest and largest Eigen values of the
following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & { - 4} & 6 \cr 2 & { - 3} & 5 \cr } } \right]$$
A
$$1.5$$ and $$2.5$$
B
$$0.5$$ and $$2.5$$
C
$$1.0$$ and $$3.0$$
D
$$1.0$$ and $$2.0$$
3
GATE CE 2015 Set 2
+2
-0.6
The two Eigen Values of the matrix $$\left[ {\matrix{ 2 & 1 \cr 1 & p \cr } } \right]$$ have a ratio of $$3:1$$ for $$p=2.$$ What is another value of $$'p'$$ for which the Eigen values have the same ratio of $$3:1$$?
A
$$-2$$
B
$$1$$
C
$$7/3$$
D
$$14/3$$
4
GATE CE 2013
Numerical
+2
-0
What is the minimum number of multiplications involved in computing the matrix product $$PQR?$$ Matrix $$P$$ has $$4$$ rows and $$2$$ columns, matrix $$Q$$ has $$2$$ rows and $$4$$ columns and matrix $$R$$ has $$4$$ rows and $$1$$ column ______.