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## Homework Statement

Question 1. Let [tex]v_{1} = \begin{bmatrix}

1\\

0\\

-1\\

0\\

\end{bmatrix}[/tex],[tex]v_{2} = \begin{bmatrix}0\\-1\\0\\1\\\end{bmatrix}[/tex], [tex]v_{3}=\begin{bmatrix}

1\\

0\\

0\\

-1\\

\end{bmatrix}[/tex]

Does {v

_{1}, v

_{2}, v

_{3}} span [tex]\mathbb{R}^4[/tex] Why or why not?

**Attempt at Question 1**

Span is just a linear combination of all the vectors. So I simply just add up the vectors and get [tex]\begin{bmatrix}

2\\

-1\\

-1\\

0\\

\end{bmatrix}[/tex]

Since the last term is a 0, therefore this must stay in [tex]\mathbb{R}^3[/tex]

**Solution to Question one**

[PLAIN]http://img87.imageshack.us/img87/5067/81744055.png [Broken]

Why are they instead asking if v

_{3}is in the span of {v

_{1}, v

_{2}, v

_{3}}? What am I doing wrong?

**Question 2**

Let [tex]v_{1} = \begin{bmatrix}

0\\

0\\

-2\\

\end{bmatrix}[/tex], [tex]v_{2}=\begin{bmatrix}0\\ -3\\ 8\\\end{bmatrix}[/tex], [tex]v_{3}=\begin{bmatrix}4\\ -1\\ -5\\

\end{bmatrix}[/tex]

Does {v

_{1}, v

_{2}, v

_{3}} span [tex]\mathbb{R}^3[/tex] Why or why not?

**Attempt**

Notice that there is a {0,0,4} which means there is no solution.

If I were to use my original method and I add the vectors I get <4, -4, 1>

Which has three nonzero entries and therefore it spans in [tex]\mathbb{R}^3[/tex]

My book is confusing me with the KEY

**Solution by book**

[PLAIN]http://img214.imageshack.us/img214/6066/81350323.png [Broken]

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