- #1
CookieSalesman
- 103
- 5
Homework Statement
Linear algebra:[/B]
Find all x in R4 space that are mapped into the zero vector for the given matrix A
A=
| 1 -4 7 -5 |
| 0 1 -4 3|
| 2 -6 6 -4|
Homework Equations
None... it's linear algebra. Don't ban me.
The Attempt at a Solution
I tried RREF on this after setting this Ax=b to zero (b = 0 vector)
|1 0 -9 7 0 |
|0 1 -4 3 0 |
|2 -6 6 -4 0 |
And I solved...
using x1=x x2=y x3=z etc... because 9x1 looks confusing
(x,y,z,w)
I have
x - 9z + 7w =0
y-4z+3w=0
The answer in the book is
z times some column (9;4;1;0) + w times some column (-7 -3 0 1)
(Nevermind the messy notation this probably isn't necessary for you anyway)
BUT I just can't get this right!
I just can't understand this somehow.
I just completely forgot how to represent this properly.
I mean technically
"
x - 9z + 7w =0
y-4z+3w=0
"
is an answer, right?
However the book just has it in this certain notation, and also the question asks "find all x" that are mapped...
But... just please help me figure out why I can't do this.
At first I was even confused that why X had four rows... Idk how to represent this. I looked in an earlier section in the book and that doesn't even help. Maybe I need some sleep. :l