1

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

+1

-0.3

Let $${c_1},.....,\,\,{c_n}$$ be scalars, not all zero, such that $$\sum\limits_{i = 1}^n {{c_i}{a_i} = 0} $$ where $${{a_i}}$$ are column vectors in $${R^{11}}.$$ Consider the set of linear equations $$AX=b$$

Where $$A = \left[ {{a_1},.....,\,\,{a_n}} \right]$$ and $$b = \sum\limits_{i = 1}^n {{a_i}.} $$

The set of equations has

2

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

+1

-0.3

Consider the system, each consisting of m linear equations in $$n$$ variables.

$$I.$$ $$\,\,\,$$ If $$m < n,$$ then all such system have a solution

$$II.$$ $$\,\,\,$$ If $$m > n,$$ then none of these systems has a solution

$$III.$$ $$\,\,\,$$ If $$m = n,$$ then there exists a system which has a solution

$$I.$$ $$\,\,\,$$ If $$m < n,$$ then all such system have a solution

$$II.$$ $$\,\,\,$$ If $$m > n,$$ then none of these systems has a solution

$$III.$$ $$\,\,\,$$ If $$m = n,$$ then there exists a system which has a solution

Which one of the following is **CORRECT**?

3

GATE CSE 2016 Set 2

Numerical

+1

-0

Suppose that the eigen values of matrix $$A$$ are $$1, 2, 4.$$ The determinant of $${\left( {{A^{ - 1}}} \right)^T}$$ is _______.

Your input ____

4

GATE CSE 2016 Set 1

Numerical

+1

-0

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

Your input ____

Questions Asked from Linear Algebra (Marks 1)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2023 (1)
GATE CSE 2022 (4)
GATE CSE 2019 (1)
GATE CSE 2018 (1)
GATE CSE 2017 Set 2 (1)
GATE CSE 2017 Set 1 (1)
GATE CSE 2016 Set 2 (2)
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GATE CSE 2015 Set 3 (1)
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GATE CSE 2004 (3)
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GATE CSE 2000 (2)
GATE CSE 1998 (1)
GATE CSE 1997 (1)
GATE CSE 1996 (2)
GATE CSE 1995 (2)
GATE CSE 1994 (2)
GATE CSE 1993 (2)

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