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Linear Algebra With Applications
Found in: Page 5
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

In exercises 1 through 10, find all solutions of the linear systems using elimination. Then check your solutions

7. x+2y+3z=1x+3y+4z=3x+4y+5z=4

The system of equation has no solution.

See the step by step solution

Step by Step Solution

Step 1:Transforming the system

To get the solution, we will transform the value ofx,y,z.

x+2y+3z=1 ......1x+3y+4z=3 ......2x+4y+5z=4 ......3Into the form x=....y=....z=...

Step 2: Eliminating the variables

In the given system of equations, we can eliminate the variables by adding or subtracting the equations.

In this system, we can eliminate the variable x from equation 2 and 3. First of all subtract the equation 1 from equation 2 and then subtract the first equation from equation 3.


Now multiply equation 2 by 2 and then subtract equation 2 from equation 3.


For whatever the value of the value 0 will never equal to 1. Thus, the given system of equations is inconsistent.

Hence, the given system of the equation has no solution.

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