I would really appreciate the help for the question below

Solve the linear equations

2x+3y+z=0

x-y+2z = 0 ( THe first equation is at the top and the second is at the bottom row in matrix form)

and hence solve

2x+3y+z=0

x-y+2z = 0

ax+y-z=0 ( respectively from top to bottom row in the matrix) for all aER.

Pleas ehelp me with this! I solved the first part with parametric equations, I got x=-7/3t and y =t and z=5/3t. However, how do I apply it to the second one? I just went about the sam way for the second one as I did the first one but I got stuck and they have to be related somehow. I only can figure out that both have the same two equations, but I'm a blockhead for anything more.

2.)Consider the system of equations

x+3y+kz=2

kx-2y+3z=k

4x-3y+10z= 5

I reduced it to my very best, I had 4 times Row =2 minus k times Row 3 to change row 2 and then for channging row 3, I had -1 times Row 3 + Row 2.

I got

[tex]\begin{bmatrix} 1 & 3 & k \\0 & 3k-8 & 12-10k \\0 & 0 & 0 \end{bmatrix}\begin{bmatrix} x \\y \\z \end{bmatrix} = $\displaystyle \begin{bmatrix} 2 \\-k \\0 \end{bmatrix}$

However, the answer had a very different form of doing the row reduction, it had subtracted the multiple of another row form some row. SOrry that I could not be more specific as the answer sheet is not with me now..please could you help me identify where I had gone wrong here?

Appreciate it loads, thank you!