- #1
vwishndaetr
- 87
- 0
Homework Statement
Ax=b where,
A = 1 -1
...-1 1
Homework Equations
a) Find Null Space N(A) and Column Space C(A)
b) For which vectors b does the system Kx=b have a solution?
c) How many solution x does the system have for any given b
The Attempt at a Solution
a)
For Null Space, I got x = 1
........1
For Column Space, I got b = span ( 1 -1 )
.........-1 1
b)
This is once again, equal to the column space.
c)
Following the similar approach as before,
Let Ax = b and Ay = b be two equations.
Ax - Ay = b - b
A(x - y) = 0
Since we solved Ax=0 for Null Space, x = 1
..........1
So, x - y = 1
...1
Now, I know it isn't only equal to that vector. Correct? Null Space is all scalar multiple and sums of that vector.
So can I now say that x - y = c 1 ?
.........1
Also by looking at that, I want to say that there are an infinite number of solutions for a given b. Because, there is an infinite number of ways to combine x and y to get the vector one one.
I am confident this time. Can someone concur?
Also, is there a thread on this forum somewhere that teaches you how to post matrices and other mathematical equations so to say the right way? Maybe a forum where you can just post a junk thread to practice?
Thanks again, I love the input! :)