In Exercises 10 through 20, use paper and pencil to identify the redundant vectors. Thus

Chapter 3, Problem 10

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QUESTION:

In Exercise, use paper and pencil to identify the redundant vectors. Thus determine whether the given vectors are linearly independent.

\(\left[\begin{array}{l}
2 \\
1
\end{array}\right],\left[\begin{array}{l}
6 \\
3
\end{array}\right]\)

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Questions & Answers

QUESTION:

In Exercise, use paper and pencil to identify the redundant vectors. Thus determine whether the given vectors are linearly independent.

\(\left[\begin{array}{l}
2 \\
1
\end{array}\right],\left[\begin{array}{l}
6 \\
3
\end{array}\right]\)

ANSWER:

Step 1 of 2

We want to find out if the given vectors are linearly dependent by finding the redundant vectors. To do this we will let:

\(\overrightarrow{v_{1}}=\left[\begin{array}{l}
2 \\
1
\end{array}\right] \text { and } \overrightarrow{v_{2}}=\left[\begin{array}{l}
6 \\
3
\end{array}\right]\)

If one is dependent we can write \(\overrightarrow{v_{2}}=c_{2} \vec{v}_{1}\)

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