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Assignment 3B PDF

This document provides instructions for Assignment 3 of the NPTEL Basic Linear Algebra 2020 course. It includes two problems involving systems of linear equations. Problem 1 involves a homogeneous system and asks the student to (a) find a value of a that requires row interchanging during Gaussian elimination, (b) find values of b that yield a nontrivial solution given constraints on a, and (c) find the general solution given additional constraints. Problem 2 involves a non-homogeneous system and asks the student to (a) row reduce the coefficient matrix, (b) solve the system, and (c) find bases for the rowspace and columnspace of the coefficient matrix. The deadline for submitting the assignment is February 19,

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153 views1 page

Assignment 3B PDF

This document provides instructions for Assignment 3 of the NPTEL Basic Linear Algebra 2020 course. It includes two problems involving systems of linear equations. Problem 1 involves a homogeneous system and asks the student to (a) find a value of a that requires row interchanging during Gaussian elimination, (b) find values of b that yield a nontrivial solution given constraints on a, and (c) find the general solution given additional constraints. Problem 2 involves a non-homogeneous system and asks the student to (a) row reduce the coefficient matrix, (b) solve the system, and (c) find bases for the rowspace and columnspace of the coefficient matrix. The deadline for submitting the assignment is February 19,

Uploaded by

Md Minhaj Ahmed Ahmed
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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NPTEL Basic Linear Algebra 2020

Assignment 3 - Subjective

Course Instructor: Prof. I. K. Rana Course TA: S. Venkitesh

Deadline: Wednesday, February 19, 2020, 23:59 IST

(1) Consider the following homogeneous system of linear equations.

x + 2y = 0, ax + 8y + 3z = 0, by + 5z = 0.

(a) Find a value of a which will make it necessary during Gaussian elimination to inter-
change rows in the coefficient matrix. [2]
(b) Suppose a does not have the value obtained in part (a). Find the values of b so that
the system has a nontrivial solution. [3]
(c) Suppsose a does not have the value obtained in part (a) and b = 100. Suppose
further that the value of a is chosen so that the solution to the system is not unique.
Find the general solution to the system. [5]

(2) Consider the following system of equations.


 
x + y + z = 2, x + 3y + 3z = 0, x + 3y + 6z = 3.

(a) Use Gaussian elimination to convert the coefficient matrix to REF. [2]
(b) Solve the system. [3]
(c) Let A denote the coefficient matrix given. The rowspace (columnspace) of A is the
set of all linear combinations of the rows (columns) of A. Find a basis of the rowspace
and the columnspace of A. [5]

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