1
GATE IN 2006
MCQ (Single Correct Answer)
+2
-0.6
A system of linear simultaneous equations is given as $$AX=b$$
where $$A = \left[ {\matrix{ 1 & 0 & 1 & 0 \cr 0 & 1 & 0 & 1 \cr 1 & 1 & 0 & 0 \cr 0 & 0 & 0 & 1 \cr } } \right]\,\,\& \,\,b = \left[ {\matrix{ 0 \cr 0 \cr 0 \cr 1 \cr } } \right]$$

Which of the following statement is true?

A
$$x$$ is a null vector
B
$$x$$ is unique
C
$$x$$ does not exist
D
$$x$$ has infinitely many values
2
GATE IN 2006
MCQ (Single Correct Answer)
+2
-0.6
A system of linear simultaneous equations is given as $$AX=b$$
where $$A = \left[ {\matrix{ 1 & 0 & 1 & 0 \cr 0 & 1 & 0 & 1 \cr 1 & 1 & 0 & 0 \cr 0 & 0 & 0 & 1 \cr } } \right]\,\,\& \,\,b = \left[ {\matrix{ 0 \cr 0 \cr 0 \cr 1 \cr } } \right]$$

Then the rank of matrix $$A$$ is

A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
3
GATE IN 2006
MCQ (Single Correct Answer)
+2
-0.6
For a given $$2x2$$ matrix $$A,$$ it is observved that $$A\left[ {\matrix{ 1 \cr { - 1} \cr } } \right] = - 1\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]$$ and
$$A\left[ {\matrix{ 1 \cr { - 2} \cr } } \right] = - 2\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]$$ then the matrix $$A$$ is
A
$$A = \left[ {\matrix{ 1 & 1 \cr { - 1} & { - 2} \cr } } \right]\,\,\left[ {\matrix{ 1 & 0 \cr 1 & 2 \cr } } \right]\,\,\left[ {\matrix{ 2 & 1 \cr { - 1} & { - 1} \cr } } \right]$$
B
$$A = \left[ {\matrix{ 1 & 1 \cr { - 1} & { - 2} \cr } } \right]\,\,\left[ {\matrix{ 1 & 0 \cr 1 & 2 \cr } } \right]\,\,\left[ {\matrix{ 2 & 1 \cr { - 1} & { - 1} \cr } } \right]$$
C
$$A = \left[ {\matrix{ 1 & 1 \cr { - 1} & { - 2} \cr } } \right]\,\,\left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\,\,\left[ {\matrix{ 2 & 1 \cr { - 1} & { - 1} \cr } } \right]$$
D
$$A = \left[ {\matrix{ 0 & { - 2} \cr 1 & { - 3} \cr } } \right]$$
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12