- Thread starter
- #1

#### karush

##### Well-known member

- Jan 31, 2012

- 2,657

Are the vectors

$$\left[

\begin{array}{r}

2\\1\\-2

\end{array}\right]

,\quad

\left[\begin{array}{r}

0\\2\\-2

\end{array}\right]

,\quad

\left[\begin{array}{r}

2\\3\\-4

\end{array}\right]

$$

linearly dependent or linearly independent?

$$\left[ \begin{array}{rrr|r} 2 & 0 & 2 & 0 \\ 1 & 2 & 3 & 0 \\ -2 & -2 & -4 & 0 \end{array} \right]

\sim

\left[ \begin{array}{rrr|r} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right]$$

I assume this is independent due to trivial answers

$$\left[

\begin{array}{r}

2\\1\\-2

\end{array}\right]

,\quad

\left[\begin{array}{r}

0\\2\\-2

\end{array}\right]

,\quad

\left[\begin{array}{r}

2\\3\\-4

\end{array}\right]

$$

linearly dependent or linearly independent?

$$\left[ \begin{array}{rrr|r} 2 & 0 & 2 & 0 \\ 1 & 2 & 3 & 0 \\ -2 & -2 & -4 & 0 \end{array} \right]

\sim

\left[ \begin{array}{rrr|r} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right]$$

I assume this is independent due to trivial answers

Last edited: