Question

Are the vectors (ˆi+ˆj+ˆk),(2ˆi+3ˆj−ˆk) and (−ˆi−2ˆj+2ˆk) are linearly dependent ?

Answer 1

Answer:

Yes, they are linearly dependent.

For instance, u - v - w = 0.

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Step-by-step explanation:

Perform row operations on the matrix of coefficients.  If you get a zero row, then yes, the vectors are linearly dependent, otherwise no they're not.

$\displaystyle\left(\begin{array}{ccc}1&1&1\\2&3&-1\\-1&-2&2\end{array}\right)\\ \\\rightarrow\left(\begin{array}{ccc}1&1&1\\0&1&-3\\0&-1&3\end{array}\right)\\ \\\rightarrow\left(\begin{array}{ccc}1&1&1\\0&1&-3\\0&0&0\end{array}\right)$

Yes, the vectors are linearly dependent.

Calling them u, v, w, in that order, the row operations showed that:

u - v - w = 0.