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# 2/11/22, 2:07 PM Quiz: M3.C1: Quiz: On Modules 1-2 https://sit.instructure.com/courses/58579/quizzes/68968/take 1/3 M3.C1: Quiz: On Modules 1-2 Started: Feb 11 at 2:06pm Quiz Instructions This quiz is...

2/11/22, 2:07 PM Quiz: M3.C1: Quiz: On Modules 1-2
https:
sit.instructure.com/courses/58579/quizzes/68968/take 1/3
M3.C1: Quiz: On Modules 1-2
Started: Feb 11 at 2:06pm
Quiz Instructions
This quiz is aimed at helping you to have a comprehensive revision of the basics of linear alge
a that
have been covered in Module 1 and Module 2.

Instructions:
1. Give yourself a distraction-free 60 minutes to take the quiz in one sitting.
2. Make sure to submit before the end of the allotted 60 minutes, otherwise the quiz closes with an
autosubmit.
4. You have only three submissions for the quiz. Submit only after careful review of your answers.
25 ptsQuestion 1
The dimension of the left null-space is 4.
The dimension of the null space of A is 2.
Every element in the row space is mapped to a unique element in the column space by the
linear transformation given by A.
The dimension of the row space is 4.
The dimension of the null space of A is 4.
Consider a matrix whose rank is 4. Pick up the co
ect statement from
the following.
25 ptsQuestion 2
Pick the co
ect statements regarding eigenvalues, eigenvectors, and eigen-
decomposition.
2/11/22, 2:07 PM Quiz: M3.C1: Quiz: On Modules 1-2
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For a symmetric matrix the eigenvalues are real.
For a symmetric positive definite matrix, the eigenvalues are all positive.
Every square matrix has an eigen-decomposition.
If a square matrix has all distinct eigenvalues, then it will have an eigen-decomposition
A matrix having an eigen-decomposition is invertible.
25 ptsQuestion 3
Division by small numbers in an iterative process is a potential source of instability.
The relative e
or in any elementary arithmetic operation is bounded above by machine
precision.
There are as many numbers between 1 and 2 as there are between 3 and 4.
Machine precision epsilon is the smallest decimal number that could be represented on the
computer.
Most of the decimal numbers are concentrated around zero.
Pick the co
ect statements on the 64-bit machine representation of numbers.
25 ptsQuestion 4
A square matrix and its transpose both have the same set of eigenvalues.
It is possible to have , even when .
If the trace of a matrix is zero, then it must be a singular matrix.
A real square matrix has only real eigenvalues.
Pick all the co
ect statements from below.
2/11/22, 2:07 PM Quiz: M3.C1: Quiz: On Modules 1-2
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Quiz saved at 2:06pm
If , then the matrix rotates the vector by more than .
The matrix is positive definite if is positive definite.
Submit Quiz

## Solution

Rajeswari answered on Feb 13 2022
Eigne values assignment
Qno.1
i. True
ii. True
iii. True
iv. False
v. False
Qno.2
i. True
ii. True
iii. False
iv. True
v. False
Qno.3
i. False
ii. False
iii. True
iv. True
v. False
Qno.4
i. True
ii. True
iii. False
iv. False
v. True
SOLUTION.PDF