Please Obi-sci-kenobi. You're my only hope. I know this
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Please Obi-sci-kenobi. You're my only hope.
I know this is "homework help question", but I really want to learn the method on how to solve matrices.
This is just one of my problems, but I can't seem to solve it with elementary row operations. An online calculator can solve it, but I can't figure it out. Is the system inconsistent?
The last column is obviously the right side of the equation. Everything to the left are obviously the coefficients.
2 1 3 2 0 1
0 0 1 1 2 1
0 0 0 0 3 0
I managed to simplify it to this:
2 1 1 0 0 0
0 0 1 1 0 1
0 0 0 0 1 0
but I can't figure out what to do from here.
>>7800858
a solution:
[math] \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \\ 0 \end{bmatrix} [/math]
>>7800858
>2 1 1 0 0 0
>0 0 1 1 0 1
>0 0 0 0 1 0
2 1 1 0 0 -1
0 0 1 1 0 1
0 0 0 0 1 0
>>7800858
>2 1 1 0 0 0
>0 0 1 1 0 1
>0 0 0 0 1 0
row-1 looks incorrect, should be
2 1 2 1 0 0
>>7800883
Yeah you're right
But now what?
>>7800858
>how to solve matrices
Can we stop blindly throwing the word "solve" around anytime there's math involved?
>>7801042
At the bottom I referred to equations, implying that this is an augmented matrix
I am trying to solve a system of equations
>>7800858
The relevant matrix is 3x5, rank 3. You will have a 2 dimensional space of solutions. Find one solution p, and a basis for the kernel of the matrix k1,k2, the solutions will be p + c1 k1 + c2 k2.
Or something.
>>7801985
To find a particular solution, consider the first two rows, columns 2
and 3 (plus augmentation):
1 3 1
0 1 1
A solution is [-2,1]. So for the original, [0,-2,1,0,0] is a solution.
Now find the kernel.