1. ## Elementary row operations

Find solutions using elementary row operations

x+2y+z=0
2x+5y+2x=0
x+4y+7z=0
x+3y+3z=0

I subtracted 2 times the 1st equation from the 2nd to get y=0 and I subtracted the 4th eq from equation 3 to get y+4z=0, so z also equals 0. X would also equal 0, but did I do enough steps to qualify for elementray row operations? I don't want to lose points because I missed steps.

2. Originally Posted by antman
Find solutions using elementary row operations

x+2y+z=0
2x+5y+2x=0
x+4y+7z=0
x+3y+3z=0

I subtracted 2 times the 1st equation from the 2nd to get y=0 and I subtracted the 4th eq from equation 3 to get y+4z=0, so z also equals 0. X would also equal 0, but did I do enough steps to qualify for elementray row operations? I don't want to lose points because I missed steps.
Yes that's fine.

3. I'll assume Prove It followed your work correctly. I just wanted to see if you realize that elementary row operations refer to a matrix. The coefficients of all the variables are taken in order and the last entry is the constant, which are all 0 here. So if your first equation is like ax+by+cz=d, then the matrix row would be [a b c d]. You are trying to get them in the form of two out of three of a,b and c being zero and the other one being 1 and then d can be whatever. So if the first row is "solved" it should be in the form of [1 0 0 x_a], where x_a is the value of x. You are doing this essentially but I didn't know if you really got the connection to a matrix. I guess this also depends on how your teacher is teaching this.