Solving System of Linear Equations: Where is the Mistake?

In summary, The conversation discusses finding solutions for a system of linear equations using Cramer's Rule and the use of cofactors to check the accuracy of the solutions. The correct solutions are x = 1/5, y = 3/5, and z = 1, with a determinant of 30 instead of 20.
  • #1
Nylex
552
2
It won't work and I don't see what I'm doing wrong.

Find the solutions of the following system of linear equations:

x + 3y - z = 1
2x + y + 2z = 3
5x + z = 2

I put these into the form Ax = b, where

A = (1 3 -1)
(2 1 2 )
(5 0 1 )

x = (x)
(y)
(z)

b = (1)
(3)
(2)

I worked out det A = 20.

Cramer's rule says the solutions are given by:

x = (1/det A) | 1 3 -1 | => x = 1/10
| 3 1 2 |
| 2 0 1 |

y = (1/det A) | 1 1 -1 | => y = 9/10
| 2 3 2 |
| 5 2 1 |

z = (1/det A) | 1 3 1 | => z = 11/10
| 2 1 3 |
| 5 0 2 |

These solutions are wrong, where have I gone wrong?? Grr.

When I work out the answers algebraically, I get x = 1/5, y = 3/5 and z = 1. These are correct.
 
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  • #2
det A is 30 not 20

marlon
 
  • #3
If you are not limited to using Cramer's Rule, I always find that just computing the cofactors of the matrix is much easier... and also a good way to check if your Cramer's Rule method is correct.
 
  • #4
marlon said:
det A is 30 not 20

marlon

ARGH, thank you.

Theelectricchild said:
If you are not limited to using Cramer's Rule, I always find that just computing the cofactors of the matrix is much easier... and also a good way to check if your Cramer's Rule method is correct.

I didn't understand cofactors :(.
 

Related to Solving System of Linear Equations: Where is the Mistake?

What is a system of linear equations?

A system of linear equations is a set of two or more equations that involve the same set of variables. The goal is to find the values of the variables that satisfy all of the equations simultaneously.

What are some common mistakes made when solving a system of linear equations?

Some common mistakes include forgetting to distribute coefficients, making sign errors, and dropping or adding terms when combining equations.

How can I check if I made a mistake while solving a system of linear equations?

You can check for mistakes by substituting the values you found into each equation and seeing if they satisfy the equation. Additionally, you can also use the method of elimination to solve the system and see if you get the same answer.

What is the best method for solving a system of linear equations?

The best method for solving a system of linear equations depends on the specific equations and variables involved. Some common methods include substitution, elimination, and graphing. It is important to choose a method that is efficient and accurate for your particular system.

What should I do if I am still unable to find the mistake in my system of linear equations?

If you are still unable to find the mistake, it may be helpful to have someone else look at your work or to try a different method for solving the system. You can also use online resources or consult a math tutor for assistance.

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