GATE IN 2005 | Linear Algebra Question 20 | Engineering Mathematics

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

Identity which one of the following is an eigen vectors of the matrix $$A = \left[ {\matrix{ 1 & 0 \cr { - 1} & { - 2} \cr } } \right]$$

$${\left[ {\matrix{ { - 1} & 1 \cr } } \right]^T}$$

$${\left[ {\matrix{ { 3} & -1 \cr } } \right]^T}$$

$${\left[ {\matrix{ { 1} & -1 \cr } } \right]^T}$$

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

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

Let $$A$$ be $$3 \times 3$$ matrix with rank $$2.$$ Then $$AX=O$$ has

only the trivial solution $$X=O$$

one independent solution

two independent solutions

three independent solutions

GATE IN 2001

MCQ (Single Correct Answer)

-0.3

The necessary condition to diagonalize a matrix is that

all its eigen values should be distinct

its eigen vectors should be independent

its eigen values should be real

the matrix is non-singular

GATE IN 2000

MCQ (Single Correct Answer)

-0.3

The rank of matrix $$A = \left[ {\matrix{ 1 & 2 & 3 \cr 3 & 4 & 5 \cr 4 & 6 & 8 \cr } } \right]$$ is

$$0$$

$$1$$

$$2$$

$$3$$

GATE IN Subjects

Engineering Mathematics