Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
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See our solution for Question 29E from Chapter 1.2 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 29E
Chapter:
Problem:
A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Suppose that such a system happens to be consistent. Explain why there must be an infinite number of solutions.
Step-by-Step Solution
Given Information
We are given that an underdetermined system is consistent, we have to prove that there must be an infinite number of solutions.
Step-1:
we know that an underdetermined system has more variables than the number of equations. if the number of equations are less, then we have to select at least one of the variable as free. The free variable can have infinite number of values, thus there can be infinite solutions.
Infinite Number of solutions
We are given that an underdetermined system is consistent, we have to prove that there must be an infinite number of solutions.
Step-1:
we know that an underdetermined system has more variables than the number of equations. if the number of equations are less, then we have to select at least one of the variable as free. The free variable can have infinite number of values, thus there can be infinite solutions.
Infinite Number of solutions