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15.3 verify that dim(NS(A)) + Rank(A) = 5

karush

Well-known member
Jan 31, 2012
2,648
15.3 For the matrix
$$A=\begin{bmatrix}
1 & 0 &0 & 4 &5\\
0 & 1 & 0 & 3 &2\\
0 & 0 & 1 & 3 &2\\
0 & 0 & 0 & 0 &0
\end{bmatrix}$$
(a)find a basis for RS(A) and dim(RS(A)).
ok I am assuming that since this is already in row echelon form, its nonzero rows form a basis for RS(A) then
So...
$$RS(A)=(1,0,0,4,5),\quad(0,1,0,3,2),\quad(0,0,1,3,2)$$
also
dim(RS(A))= ??

(b)verify that dim(NS(A)) + Rank(A) = 5.

ok I am a little unsure what this means