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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

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

A certain homogeneous system of linear equations in three unknowns (see Exercise 65) has a solution ( 1 , 2 , 0 ) . Is this solution unique? Explain.

To determine

Whether the solution (1,2,0) is unique for homogenous system of linear equations in three variables.

Explanation

Given Information:

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

A homogenous system of linear equations in three variables has a solution (1,2,0).

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.

Now recall the given condition of the system of equations which says that a homogenous system of linear equations in three variables has a solution (1,2,0)

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