Question

For which values of b are the vectors (3, b), (6, b-1) linearly independent?

Answer 1

terminology ... what does it mean to be linearly independant?

Answer 2

Sorry,, I went on working some other probs where I didn't have to figure out the value of b. I still have quite a few though that are the same type as my posted question...explanation would be helpful. See the attachment regarding terminology.

Answer 3

according to the text there; the number of vectors in the space is important; <x,y> would suggest R^2 to me.

since we have 2 vectors lets set them up in the matrix by rows:
\[\left(
\begin{array}c
3&b\\
6&b-1\\
\end{array}
\right)\]
a 2x2 matrix can easily be solved for the "det".

3(b-1) - 6(b) not= 0

id say determine the values for b and exclude them

3b -3 -6b = 0

-3b -3 = 0

-3b = 3

b = -1; this would be a bad case according to the text you provided.

Answer 4

gotcha! Form a matrix with the vector, find the determinant, then determine whether or not we want that value included or excluded depending on if we're talking about independent or dependent linearity. Thanks a bunch!