- #1

karush

Gold Member

MHB

- 3,269

- 5

nmh{780}

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

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

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