GATE CSE 2016 Set 1 | Linear Algebra Question 28 | Discrete Mathematics

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Let $${a_n}$$ be the number of $$n$$-bit strings that do NOT contain two consecutive $$1s.$$ Which one of the following is the recurrence relation for $${a_n}$$?

$${a_n} = {a_{n - 1}} + 2{a_{n - 2}}$$

$${a_n} = {a_{n - 1}} + {a_{n - 2}}$$

$${a_n} = 2{a_{n - 1}} + {a_{n - 2}}$$

$${a_n} = 2{a_{n - 1}} + 2{a_{n - 2}}$$

GATE CSE 2016 Set 1

Numerical

-0

Two eigenvalues of a $$3 \times 3$$ real matrix $$P$$ are $$\left( {2 + \sqrt { - 1} } \right)$$ and $$3.$$ The determinant of $$P$$ is _______.

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GATE CSE 2015 Set 1

Numerical

-0

In the LU decomposition of the matrix $$\left[ {\matrix{ 2 & 2 \cr 4 & 9 \cr } } \right]$$, if the diagonal elements of U are both 1, then the lower diagonal entry $${l_{22}}$$ of L is ________.

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GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

In the given matrix $$\left[ {\matrix{ 1 & { - 1} & 2 \cr 0 & 1 & 0 \cr 1 & 2 & 1 \cr } } \right],$$ one of the eigenvalues is $$1.$$ The eigen vectors corresponding to the eigen value $$1$$ are

$$\left\{ {\alpha \left( {4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

$$\left\{ {\alpha \left( { - 4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

$$\left\{ {\alpha \left( {\sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

$$\left\{ {\alpha \left( { - \sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$

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