GATE CSE concept:system-linear-equations PYQs & Answers

Questions 1–4 of 4. Imported answers require independent review unless marked reviewed.

Consider the system of linear equations given below.

Suppose the values of a and b are chosen such that the system of linear equations produce multiple solutions. Then the product of a and b is __________. (answer in integer)

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Consider the given system of linear equations for variables

and

, where

is a real-valued constant. Which of the following option(s) is/are CORRECT?

Your answerSelect all correct options. You can choose more than one.

There is exactly one value of

for which the above system of equations has no solution.

There exist an infinite number of values of

for which the system of equations has no solution.

There exists exactly one value of

for which the system of equations has exactly one solution.

There exists exactly one value of

for which the system of equations has an infinite number of solutions.

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Consider a system of linear equations

where

and

. Suppose

has an LU decomposition,

, where

Which of the following statement(s) is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The system

can be solved by first solving

and then

is invertible, then both

and

are invertible.

is singular, then at least one of the diagonal elements of

is zero.

is symmetric, then both

and

are symmetric.

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Let

be any

matrix, where

. Which of the following statements is/are TRUE about the system of linear equations

Your answerSelect all correct options. You can choose more than one.

There exist at least

linearly independent solutions to this system

There exist

linearly independent vectors such that every solution is a linear combination of these vectors

There exists a non-zero solution in which at least

variables are 0

There exists a solution in which at least

variables are non-zero

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GATE CSE concept:system-linear-equations PYQs

How to practice concept:system-linear-equations

Question 31

Question 23

Question 44

Question 49