Kernel, Image

  • #1
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0

Homework Statement


Find Kernel, Image, Rank and Nullity of the matrix
1 −1 1 1 
| 1 2 −1 1 |
0 3 -2 0 


Homework Equations




The Attempt at a Solution


I have reduced the matrix into rref of
3 0 1 3
0 3-2 0
0 0 0 0
But am struggling to find the column vectors which are the solutions of that, which I believe is the kernel
And then I know that the rank and nullity are the dimensions of the image and kernel respectively
 

Answers and Replies

  • #2
HallsofIvy
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Homework Helper
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The "kernel" of matrix A is the set of all vectors v such that Av= 0. If you write vector v as (a, b, c, d) then any vector in the kernel must satisfy a- b+ c+ d= 0, a+ 2b- c+ d= 0, and 3b- 2c= 0. The "image" is the set of all vectors, v, such that Ax= v for some vector x. If we write vector x as (a, b, c, d) then v must be (x, y, z) such that a- b+ c+ d= x, a+ 2b- c+ d= y, and 3b- 2c= z for some numbers a, b ,c, and d.
 

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