1
GATE EE 1998
MCQ (Single Correct Answer)
+1
-0.3
A set of linear equations is represented by the matrix equations $$Ax=b.$$ The necessary condition for the existence of a solution for this system is
A
$$A$$ must be invertible
B
$$b$$ must be linearly dependent on the columns of $$A$$
C
$$b$$ must be linearly independent on the rows of $$A$$
D
None
2
GATE EE 1998
MCQ (Single Correct Answer)
+1
-0.3
If the vector $$\left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right]$$ is an eigen vector of $$A = \left[ {\matrix{ { - 2} & 2 & { - 3} \cr 2 & 1 & { - 6} \cr { - 1} & { - 2} & 0 \cr } } \right]$$ then one of the eigen value of $$A$$ is
A
$$1$$
B
$$2$$
C
$$5$$
D
$$-1$$
3
GATE EE 1998
MCQ (Single Correct Answer)
+1
-0.3
If $$A = \left[ {\matrix{ 5 & 0 & 2 \cr 0 & 3 & 0 \cr 2 & 0 & 1 \cr } } \right]$$ then $${A^{ - 1}} = $$
A
$$\left[ {\matrix{ 1 & 0 & { - 2} \cr 0 & {1/3} & 0 \cr { - 2} & 0 & 5 \cr } } \right]$$
B
$$\left[ {\matrix{ 5 & 0 & 2 \cr 0 & { - 1/3} & 0 \cr 2 & 0 & 1 \cr } } \right]$$
C
$$\left[ {\matrix{ {1/5} & 0 & {1/2} \cr 0 & {1/3} & 0 \cr {1/2} & 0 & 1 \cr } } \right]$$
D
$$\left[ {\matrix{ {1/5} & 0 & { - 1/2} \cr 0 & {1/3} & 0 \cr { - 1/2} & 0 & 1 \cr } } \right]$$
4
GATE EE 1997
Subjective
+1
-0
Express the given matrix $$A = \left[ {\matrix{ 2 & 1 & 5 \cr 4 & 8 & {13} \cr 6 & {27} & {31} \cr } } \right]$$
as a product of triangular matrices $$L$$ and $$U$$ where the diagonal elements of the lower triangular matrices $$L$$ are unity and $$U$$ is an upper triangular matrix.
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