How to solve linear equation in matrix form if determinat is zero

In summary, solving a linear equation in matrix form with a determinant of zero can result in either no solution or an infinite number of solutions, depending on the values of both the matrix and the output vector.
  • #1
himanshu@iitp
1
0
please help me to solve linear equation in matrix form if determinant is zero
 
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  • #2
himanshu@iitp said:
please help me to solve linear equation in matrix form if determinant is zero

Welcome to the PF. Please tell us more about your question, and what you have learned so far about systems of equations and how the determinant is used in the solution. What can you say about the system of equations if the determinant is zero?
 
  • #3
In general, if Ax= y and the determinant of A is 0, there is not a single solution. There may be NO solution of an infinite number of solutions, depending upon both A and y.
 

Related to How to solve linear equation in matrix form if determinat is zero

1. How do I recognize a linear equation in matrix form?

A linear equation in matrix form will have variables represented as columns and constants represented as a separate column on the right-hand side. The variables and constants will be separated by an equal sign.

2. What does it mean if the determinant is zero in a linear equation in matrix form?

If the determinant is zero in a linear equation in matrix form, it means that the system of equations has no unique solution. This can happen if there are either no solutions or infinitely many solutions.

3. How do I solve a linear equation in matrix form if the determinant is zero?

If the determinant is zero, you can still solve the system of equations by using other methods such as substitution or elimination. However, the solution will not be unique and there may be multiple solutions or no solutions at all.

4. Can I use Gaussian elimination to solve a linear equation in matrix form with a zero determinant?

Yes, Gaussian elimination can still be used to solve the system of equations even if the determinant is zero. However, you may encounter an inconsistency in the reduced row-echelon form, indicating that the system has no solution.

5. How can I interpret the solution to a linear equation in matrix form with a zero determinant?

If the determinant is zero, the solution to the system of equations will either be a set of infinitely many solutions or no solutions at all. This can be interpreted as either an underdetermined or inconsistent system of equations.

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