- #1

karush

Gold Member

MHB

- 3,269

- 5

nmh{742}

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))

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

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))

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

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