GATE CSE 2014 Set 3 | Linear Algebra Question 35 | Discrete Mathematics

GATE CSE 2014 Set 3

Numerical

-0

If $${V_1}$$ and $${V_2}$$ are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of $${V_1}\, \cap \,\,{V_2}$$ is _________________.

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GATE CSE 2014 Set 2

Numerical

-0

If the matrix A is such that $$$A = \left[ {\matrix{ 2 \cr { - 4} \cr 7 \cr } } \right]\,\,\left[ {\matrix{ 1 & 9 & 5 \cr } } \right]$$$ then the determinant of A is equal to _________.

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GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which of the following does not equal
$$\left| {\matrix{ 1 & x & {{x^2}} \cr 1 & y & {{y^2}} \cr 1 & z & {{z^2}} \cr } } \right|?$$

$$\left| {\matrix{ 1 & {x\left( {x + 1} \right)} & {x + 1} \cr 1 & {y\left( {y + 1} \right)} & {y + 1} \cr 1 & {z\left( {z + 1} \right)} & {z + 1} \cr } } \right|$$

$$\left| {\matrix{ 1 & {x + 1} & {{x^2} + 1} \cr 1 & {y + 1} & {{y^2} + 1} \cr 1 & {z + 1} & {{z^2} + 1} \cr } } \right|$$

$$\left| {\matrix{ 0 & {x - y} & {{x^2} - {y^2}} \cr 0 & {y - z} & {{x^2} - {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$

$$\left| {\matrix{ 2 & {x + y} & {{x^2} + {y^2}} \cr 2 & {y + z} & {{x^2} + {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$

GATE CSE 2012

MCQ (Single Correct Answer)

-0.3

Let $$A$$ be the $$2 \times 2$$ matrix with elements $${a_{11}} = {a_{12}} = {a_{21}} = + 1$$ and $${a_{22}} = - 1$$. Then the eigen values of the matrix $${A^{19}}$$ are

$$1024$$ and $$-1024$$

$$1024\sqrt 2 \,i$$ and $$ - 1024\sqrt 2 $$

$$4\sqrt 2 $$ and $$-4\sqrt 2 $$

$$512\sqrt 2 $$ and $$-512\sqrt 2 $$

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