Chapter 4.2, Problem 65E

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

A system of linear equations is called homogeneous if the right-hand side of each equation in the system is 0. If a homogeneous system has a unique solution, what can you say about that solution? Why?

To determine

The nature of solution of a homogenous system which has a unique solution.

Explanation

Given Information:

A system of linear equations is called homogenous if the right hand side in each equation is 0.

Let the homogenous system have a unique solution.

Consider a system of equations which is homogenous and also this homogenous system of equations has a unique solution.

A system of equations which satisfy the given conditions can be obtained by replacing each unknown value in equation with zero as the right hand side of each equation has to be zero. This gives us a zero solution.

As the solution we are to find is a unique this comes out to be the only solution of the system of equations for the given conditions.

For example,

Consider a system of two linear homogenous equations...

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