- #1
dark494
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Homework Statement
Find a system of linear equations, with 3 unknowns, given that the solutions are the points (1,1,1) and (3,5,0) on a line.
Homework Equations
None
The Attempt at a Solution
A solution that lies on a line tells me that I'm looking at the line of intersection between 2 planes. I'm supposed to be using matrices to solve this, but I've only ever done so in the other direction: taking a system of linear equations and reducing them to reduced-row-echelon-form to find the solution set.
Since there are infinitely many solutions, there must be at least 1 dependent variable. I figured that I would need to first find the equation for the line from the points of the solution, but I ended up with this:
(x-1)/2 = (y-1)/4 = (z-1)/-1
which only confused me more. Then I tried to formulate an augmented matrix to try and find the coefficients of the linear equations, but didn't get very far after reduction, and I realized that I was still missing the right hand side of the matrix:
[a 0b 2.5c ?]
[0a b -1.5c ?]
And this is where I stand. Any help is much appreciated.