Originally Posted by

**Noxide** HELP! I want to determine if these things are independent/dependent

Don't know how to get the equations for these two:

eg of what I mean by equation

r(a, b) + r2(c, d) + r3(e, f) = 0

ra + r2c + r3e = 0

rb + r2d + r3f = 0

1.

{1, (sinx)^2, cos2x, (cosx)^2} in the **F** space, real fncts

r1(1) + r2((sinx)^2) + r3(cos2x) + r4((cosx)^2) = 0

$\displaystyle \color{red}\mbox{Do you remember the Trigonometric Pythagoras Theorem }\cos^2x +\sin^2x=1?$

from there I don't know how to group the terms so that I can set up a matrix and find out if trivial solutions exist.

2.

Similar problem as # 1 but it's with matrices in the **M** space of 2x2 matrices

all of the following matrices are 2x2

{ matrix 1, matrix 2, matrix 3}

[ 1 4 ] [ -1 5] [ -1 5]

[ - 3 ] [ -1 5] [ -1 5]

$\displaystyle \color{red}\mbox{The first one above is not a 2x2 matrix (most probably a typo), but never}$ $\displaystyle \color{red}\mbox{ mind: can you see the 2nd and 3rd matrices are identical?}$

Tonio

r1Matrix 1 + r2 Matrix 2 + r3 Matrix 3 = 0

then elim to find triv.

I just don't know how to set up the equations never seen examples.