there is a matrix A of M3X3 (K) over field K(adsbygoogle = window.adsbygoogle || []).push({});

so rank A=r , marked U as A of M3X3 (K) so AX=0

prove that dim U=3(3-r))

??

i was told that each column gives me 3-r we have 3 columns so

it 3(3-r)

i cant understand how we get 3-r out of each column??

there is W={x exists in R^3|Ax=0}

dim W=3-r

1-1 function hase Ker (t)=0

Im (T)=WxWxW

i understand that W is the kernel of T

then they say

"dim W=3-r"

so '"r" is the Image of the matrix

but why its from one column

??

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# Dimention proof question

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