Solve the given linear system by any method

Question

This is for Linear Algebra. We have been practicing Gauss-Jordan elimination in class, though the problems have been straightforward up until now (e.g. it was obvious what you had to do for certain rows to eliminate other rows in the matrix)

System of equations:

$$ v+3w-2x=0$$ $$2u+v-4w+3x=0$$ $$2u+3v+2w-x=0$$ $$-4u-3v+5w-4x=0$$

As a matrix it would look like this:

\begin{bmatrix} 0 & 1 & 3 & -2 & 0\\ 2 & 1 & -4 & 3 & 0\\2 & 3 & 2 & -1 & 0\\-4 & -3 & 5 & -4 & 0 \end{bmatrix}

I realize that this is a homogeneous system; the system will be consistent. I simply do not know where I should start. If anyone could help with the first step or two, I would be grateful!

Answer 1

i will start with the first steps multiplying the second equation by (-1) and adding to the first $$-2v-6w+4x=0$$ multiplying the first one by 2 and adding to the third one: $$-v-3w-2x=0$$ can you proceed?

Answer 2

Here is a step by step solution:

There's no secret to row reduction. It takes practice to get good at it. If there are fractions, then it will get tedious. But, if you're truly stuck, then just use a computer. On the site http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref , enter the number of rows as 4 and columns as 5, for this example.

In reality, it's silly to do row reduction by hand. In practicality, many math profs have an inexplicable hostility toward calculators and computers, so do them all by hand to prepare for tests.