Can't Row Reduce Matrix - Finding Nullspace and Imagespace

[mr_coffee]

Hello everyone...
I have the following matrix:
A =
-1 -4 1
7 -9 0
10 3 -3
-9 1 2

I can't row reduce this sucker! This isn't an agumented matrix i don't think, so i can't just take the square matrix and then find the inverse and mutliply it by vector b to find the values of a, b, c, d; So because i can't do this, I'm getting suck on figuring out the Nullspace and image space. What is the procedure to find the null and image space of a matrix that isn't nxn?

I'm trying to check it with maple ( a math program ) to see if there but i created the matrix, did all that good stuff now typed in Nullspace(A) mod P; what mod am i suppose to use, they didn't explain that part. But i'd rather have an explanation than a program doing it for me. Thanks.

 

[Galileo]

Why can't you row reduce it? Just use Gaussian elimination. This matrix can be reduced to Jordan-form in 2 steps.

 

[HallsofIvy]

Or you can just think of the null space as (x,y,z) satisfying
x- 4y+ z= 0
7x-9y= 0
10x+ 3y- 3z= 0
-9x+ y+ 2z= 0

What x, y, z satisfy all four of those?

 

[Hurkyl]

The procedure to find the image and nullspace of a nonsquare matrix should be exactly the same as for a square matrix.