How are the 2 vectors linearly dependent or linearly independent?

The question is

Examine whether the vector i-j+2k,2i+j-3k, 2i-5j+k are linearly independent or linearly dependent?

Printable View

- Jan 9th 2009, 03:27 AMrshekhar.inVector
How are the 2 vectors linearly dependent or linearly independent?

The question is

Examine whether the vector i-j+2k,2i+j-3k, 2i-5j+k are linearly independent or linearly dependent? - Jan 9th 2009, 04:46 AMDeMathQuote:

Examine whether the vector i-j+2k,2i+j-3k, 2i-5j+k are linearly independent or linearly dependent?

If a determinant is equal to 0, then vectors are linearly dependent, and conversely, vectors are linearly independent if a determinant is not equal to 0.

For your problem $\displaystyle i-j+2k, 2i+j-3k, 2i-5j+k$ it must be $\displaystyle \left| {\begin{array}{*{20}{c}}1 & { - 1} & 2 \\2 & 1 & { - 3} \\2 & { - 5} & 1 \\\end{array} } \right|$.