Finding System Solutions of the system Ax=0; A being a matrix

[gpax42]

Homework Statement

Find all solutions of the system Ax=0
where A = the 3x3 matrix

[1 3 2]
[2 6 9]
[2 8 8]

Homework Equations

not really sure what equations to include

The Attempt at a Solution

wasnt positive how to go about answering this question because I am not sure what its asking for...

i turned "x" into a 3x1 matrix consisting of x₁, x₂ and x₃ and tried to solve the system of equations...

1x₁ + 3x₂ + 2x₃ = 0
2x₁ + 6x₂ + 9x₃ = 0
2x₁ + 8x₂ + 9x₃ = 0

after trying to solve this as a linear system of equations problem, i ended getting that each value (x₁, x₂, x₃) was equal to 0... is this anywhere close to a correct approach to this problem? Thanks for any help you have to offer

 

[rochfor1]

Yes, since this matrix is indeed invertible.

 

[Mark44]

Do you know about row operations for reducing a matrix? If you do, using them to reduce your matrix would be simpler than solving three equations in three unknowns.

 

[gpax42]

My class learned about row operations today but I didn't think to apply them because I began this problem yesterday...

Thanks for your advice

 

[HallsofIvy]

If A is invertible, then the only solution to Ax= 0 is x= 0.

 

[radou]

after trying to solve this as a linear system of equations problem, i ended getting that each value (x₁, x₂, x₃) was equal to 0... is this anywhere close to a correct approach to this problem? Thanks for any help you have to offer

This is a linear system of equation which is equivalent to the matrix representation of the problem. And yes, your solution is correct, as far as I checked.