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15.3 RS(A) dim(RS(A)) dim(NS(A)) + Rank(A) = 5.

karush

Well-known member
Jan 31, 2012
2,648
For the matrix
$$\begin{bmatrix}
1 & 0 &0 & 4 &5\\
0 & 1 & 0 & 3 &2\\
0 & 0 & 1 & 3 &2\\
0 & 0 & 0 & 0 &0
\end{bmatrix}$$
(a) find a basis for RS(A)

ok this is already in rref and we have 3 pivots in $C_1,C_2,C_3$
so is $$RS(A)= \begin{bmatrix} 1\\0\\0\\0 \end{bmatrix}
, \begin{bmatrix} 0\\1\\0\\0 \end{bmatrix}
, \begin{bmatrix} 0\\0\\1\\0 \end{bmatrix}$$

(b) derive dim(RS(A)) :confused:

(c) Verify that dim(NS(A))+Rank(A)=5. :confused: