1. I do not understand the question , nor your notation
Are the [5 a -2] [5 102] etc supposed to be rows of the first matrix ?
Why are there only 2 elements in [5 102] , when all others have 3 elements?
What does 8R1 - R2 --> = R2 mean
does it say: 8 times row 1 - row 2 becomes a new row 2 ?
2.
-1 1 1 0
3 2 5 18
15 10 25 89
1 -1 -1 0
3 2 5 18
15 10 25 89
notice if we divide the third by 5 we get
3 2 5 89/5
So the last two are parallel planes and the first plane will cut these two, resulting in 2 parallel lines
(I am not familiar with your terminology in C and D
we can rule out A and B, and since there is a solution of two parallel lines, we can rule out D
So by the process of elimination....
3.
1 1 -1 3
1 -1 -2 6
2 -1 1 3
1 1 -1 3
0 2 1 -3 -- I did #1 - #2
0 3 -3 3 -- I did 2 x #1 - #3
1 1 -1 3
0 1 -4 6 -- I did #3 - #2
0 1 -1 1 -- I did #3 รท 3
1 1 -1 3
0 1 -4 6
0 0 3 -5 -- I did #3 - #2
from that I read: 3z = -5
z = -5/3
from the 2nd: y - 4z = 6
y + 20/3 = 6
y = -2/3
in the 1st:
x +y-z=3
x - 2/3 + 5/3 = 3
x = 2
I get (2, -2/3 , -5/3)
which I subbed into all three equations and it worked!