Solving for k in a Homogenous System

  • Thread starter HKP
  • Start date
In summary, a matrice problem involves using matrices to perform mathematical operations and solve equations. To solve these problems, one must have a basic understanding of matrix operations and properties, and can use resources such as textbooks, online tools, or calculators. Matrice problems have various applications in different fields, such as economics and engineering, and can be used to solve systems of equations. Some tips for solving matrice problems include double-checking your work and breaking down the problem into smaller steps. Regular practice can also help improve skills in solving these types of problems.
  • #1
HKP
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Homework Statement


Find all values of k such that the following homogenous system has non-trivial solutinos:
kx + 2y + 2z = 0
x + 2y + 2z = 0
4x + (k-1)y +2z = 0

Homework Equations





The Attempt at a Solution


I put it into matrix form ( k 2 2 0
1 2 2 0
4 (k-1) 2 0 )
Then i subtracted row 2 from row 1 to get
k 2 2 0
(1-k) 0 0 0
4 (k-1) 2 0

Then i said if k=1 then there are infinite many solutions.

I don't know where to go from that.
 
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  • #2
No, that's not right at all! I think you even forgot to interchange row 2 with row 1 in order to introduce a leading 1 in a11.
 

Related to Solving for k in a Homogenous System

1. What is a matrice problem?

A matrice problem is a mathematical problem that involves matrices, which are rectangular arrays of numbers or symbols. These problems often involve operations such as addition, subtraction, multiplication, and inversion of matrices.

2. How do I solve a matrice problem?

To solve a matrice problem, you will need to have a basic understanding of matrix operations and properties. You can follow the steps outlined in your textbook or online resources, or use a graphing calculator or software to assist you.

3. What are some common applications of matrice problems?

Matrice problems have various applications in fields such as economics, engineering, computer science, and physics. They are used to model and solve real-life problems involving systems of equations, transformations, and data analysis.

4. Can I use matrices to solve systems of equations?

Yes, matrices can be used to solve systems of equations. This is known as the Gauss-Jordan elimination method, where the system of equations is represented in matrix form and then manipulated to obtain the solution.

5. Are there any tips for solving matrice problems?

One tip for solving matrice problems is to always check your work and make sure your matrix operations are correct. It is also helpful to break down the problem into smaller steps and to practice regularly to improve your skills.

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