ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: jasoN- on October 30, 2010, 10:45:25 am

Title: Regarding linear independence
Post by: jasoN- on October 30, 2010, 10:45:25 am: If a question asks to prove that vectors a, b and c are linearly independent,
can I prove that they are NOT dependent, hence independent?
ie. if a = mb + nc, there are no m, n values that satisfy the vectors, hence independent (or is this the only way, idk)
thanks
Title: Re: Regarding linear independence
Post by: jasoN- on October 30, 2010, 11:03:28 am: another question
is this correct?
Scalar resolute of $\tilde{a}$ in the direction of (or parallel to) $\tilde{b}$ is $\tilde{a} \cdot \tilde{\hat{b}}$
Scalar resolute of $\tilde{a}$ perpendicular to $\tilde{b}$ is $| \tilde{a} - (\tilde{a} \cdot \tilde{\hat{b}}) \tilde{\hat{b}} |$
quite weird.
Title: Re: Regarding linear independence
Post by: Martoman on October 30, 2010, 11:15:11 am: Right and right.

For the first, you could also show m and n are either 0.

That *scalar* resolute always trips me up, i keep in onthing its a.b/b.b
Title: Re: Regarding linear independence
Post by: jasoN- on October 30, 2010, 11:59:44 am: thanks, i'd rather stick with one method approach :)
well you're not gonna have to remember the scalar resolute since we only have exam 2 left :D