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Can you find an image and nullspace of a nonsquare matrices? running into problems!

  1. Nov 16, 2005 #1
    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.
     
  2. jcsd
  3. Nov 17, 2005 #2

    Galileo

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    Why can't you row reduce it? Just use Gaussian elimination. This matrix can be reduced to Jordan-form in 2 steps.
     
  4. Nov 17, 2005 #3

    HallsofIvy

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    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?
     
  5. Nov 17, 2005 #4

    Hurkyl

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