Solve the system of equations?

In summary, the conversation is about solving a system of equations using Gaussian or Gauss-Jordan elimination. The equations are x1-3x2-2x3=0, -x1+2x2+x3=0, and 2x1+4x2+6x3=0. The attempt at a solution involved performing row operations to reduce the equations, but the resulting answer did not match the one in the book, which was t*[1, 1, -1]. It was suggested to check if the book's answer satisfies the equations, and to complete the row reduction to find a free variable and solve for the others in terms of it.
  • #1
Math9999

Homework Statement


Solve the system of equations
x1-3x2-2x3=0
-x1+2x2+x3=0
2x1+4x2+6x3=0
using either Gaussian or Gauss-Jordan elimination.

Homework Equations


None.

The Attempt at a Solution


R1+R2, I got
x1-3x2-2x3=0
-x2-x3=0
2x1+4x2+6x3=0
-----------------------------------------------------------------------
-2R1+R3, I got
x1-3x2-2x3=0
-x2-x3=0
10x2+10x3=0
----------------------------------------------------------------------
10R2+R3, I got
x1-3x2-2x3=0
-x2-x3=0
--------------------------------------------------------------------
Once I did the calculation, it doesn't match the answer from the book. Because I got x2=0 and x3=0 so therefore x1=0. But the answer in the book says t*[1, 1, -1]. Can anyone tell me what's wrong and how to get the right answer?
 
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  • #2
Does the answer in the book check with the equations? I'd start there.

All your equations are equal to zero, so there exists a solution iff the determinant of the coefficients is zero.
 
  • #3
Yes, when I plug in [1, 1, -1] into the given equations, it matches. But I don't know how they got the t variable in the answer.
 
  • #4
You haven't completed the row reduction. When you do you should find a free variable that you can let be anything and get the others in terms of it.
 

FAQ: Solve the system of equations?

What is a system of equations?

A system of equations is a set of two or more equations that share common variables. The solution to a system of equations is a set of values that make all of the equations true when substituted into the equations.

How do you solve a system of equations?

There are several methods for solving a system of equations, including substitution, elimination, and graphing. The method chosen depends on the specific system of equations and its complexity.

Can a system of equations have more than one solution?

Yes, a system of equations can have no solution, one solution, or infinitely many solutions. The number of solutions depends on the number of equations and variables in the system.

What are the different types of solutions for a system of equations?

The three types of solutions for a system of equations are consistent, inconsistent, and dependent. A consistent system has at least one solution, an inconsistent system has no solutions, and a dependent system has infinitely many solutions.

Why is solving a system of equations important?

Solving a system of equations is important because it allows us to find the relationship between multiple variables and make predictions about their values. It is also a fundamental concept in mathematics and is used in many real-life applications, such as in physics and engineering.

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