1
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
Consider the following system of linear equations
$$$\left[ {\matrix{
2 & 1 & { - 4} \cr
4 & 3 & { - 12} \cr
1 & 2 & { - 8} \cr
} } \right]\left[ {\matrix{
x \cr
y \cr
z \cr
} } \right] = \left[ {\matrix{
\alpha \cr
5 \cr
7 \cr
} } \right]$$$
Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of $$\alpha $$, does this system of equations have infinitely many solutions?
2
GATE CSE 2002
Subjective
+2
-0
Obtain the eigen values of the matrix
$$$A = \left[ {\matrix{
1 & 2 & {34} & {49} \cr
0 & 2 & {43} & {94} \cr
0 & 0 & { - 2} & {104} \cr
0 & 0 & 0 & { - 1} \cr
} } \right]$$$
3
GATE CSE 1998
MCQ (Single Correct Answer)
+2
-0.6
Consider the following determinant
$$$\Delta = \left| {\matrix{
1 & a & {bc} \cr
1 & a & {ca} \cr
1 & a & {ab} \cr
} } \right|$$$
Which of the following is a factor of $$\Delta $$ ?
4
GATE CSE 1998
MCQ (Single Correct Answer)
+2
-0.6
The rank of the matrix given below is:
$$$\left[ {\matrix{
1 & 4 & 8 & 7 \cr
0 & 0 & 3 & 0 \cr
4 & 2 & 3 & 1 \cr
3 & {12} & {24} & {2} \cr
} } \right]$$$
Questions Asked from Linear Algebra (Marks 2)
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