GATE PI 2012 | Linear Algebra Question 5 | Engineering Mathematics

GATE PI 2012

MCQ (Single Correct Answer)

-0.6

$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$
The system of algebraic equations given above has

a unique solution of $$x=1,y=1$$ and $$z=1$$

only the two solutions of $$x=1, y=1, z=1$$ and $$x=2, y=1, z=0$$

infinite number of solutions.

no feasible solution.

GATE PI 2011

MCQ (Single Correct Answer)

-0.6

If a matrix $$A = \left[ {\matrix{ 2 & 4 \cr 1 & 3 \cr } } \right]$$ and matrix $$B = \left[ {\matrix{ 4 & 6 \cr 5 & 9 \cr } } \right]$$ the transpose of product of these two matrices i.e., $${\left( {AB} \right)^T}$$ is equal to

$$\left[ {\matrix{ {28} & {19} \cr {34} & {47} \cr } } \right]$$

$$\left[ {\matrix{ {19} & {34} \cr {47} & {28} \cr } } \right]$$

$$\left[ {\matrix{ {48} & {33} \cr {28} & {19} \cr } } \right]$$

$$\left[ {\matrix{ {28} & {19} \cr {48} & {33} \cr } } \right]$$

GATE PI 2009

MCQ (Single Correct Answer)

-0.6

The value of $${x_3}$$ obtained by solving the following system of linear equations is $$${x_1} + 2{x_2} - 2{x_3} = 4$$$ $$$2{x_1} + {x_2} + {x_3} = - 2$$$ $$$ - {x_1} + {x_2} - {x_3} = 2$$$

$$-12$$

$$-2$$

$$0$$

$$12$$

GATE PI 2008

MCQ (Single Correct Answer)

-0.6

The eigen vector pair of the matrix $$\left[ {\matrix{ 3 & 4 \cr 4 & { - 3} \cr } } \right]$$ is

$$\left[ {\matrix{ 2 \cr 1 \cr } } \right]\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]$$

$$\left[ {\matrix{ 2 \cr 1 \cr } } \right]\left[ {\matrix{ 1 \cr 2 \cr } } \right]$$

$$\left[ {\matrix{ { - 2} \cr 1 \cr } } \right]\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]$$

$$\left[ {\matrix{ { - 2} \cr 1 \cr } } \right]\left[ {\matrix{ 1 \cr 2 \cr } } \right]$$