GATE ME 2017 Set 2 | Linear Algebra Question 4 | Engineering Mathematics

GATE ME 2017 Set 2

Numerical

-0

Consider the matrix $$A = \left[ {\matrix{ {50} & {70} \cr {70} & {80} \cr } } \right]$$ whose eigenvectors corresponding to eigen values $${\lambda _1}$$ and $${\lambda _2}$$ are $${x_1} = \left[ {\matrix{ {70} \cr {{\lambda _1} - 50} \cr } } \right]$$ and $${x_2} = \left[ {\matrix{ {{\lambda _2} - 80} \cr {70} \cr } } \right],$$ respectively. The value of $$x_1^T{x_2}$$ is ________

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GATE ME 2016 Set 3

Numerical

-0

The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{ 2 & 1 & 0 \cr 0 & 2 & 0 \cr 0 & 0 & 3 \cr } } \right]$$ is ________.

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GATE ME 2015 Set 3

MCQ (Single Correct Answer)

-0.6

For a given matrix $$P = \left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right],$$ where $$i = \sqrt { - 1} ,$$ the inverse of matrix $$P$$ is

$${1 \over {24}}\left[ {\matrix{ {4 - 3i} & i \cr { - i} & {4 + 3i} \cr } } \right]$$

$${1 \over {25}}\left[ {\matrix{ i & {4 - 3i} \cr {4 + 3i} & i \cr } } \right]$$

$${1 \over {24}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$

$${1 \over {25}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$

GATE ME 2013

MCQ (Single Correct Answer)

-0.6

Choose the CORRECT set of functions, which are linearly dependent.

$$\sin x,\,{\sin ^2}x$$ and $${\cos ^2}x$$

$$\cos x,\sin x$$ and $$\tan x$$

$$\cos \,2x,{\sin ^2}x$$ and $${\cos ^2}x$$

$$\cos \,2x,\sin x$$ and $$\cos x$$