- #1

member 731016

- Homework Statement
- Please see below

- Relevant Equations
- Please see below

For part(b),

My solution is,

##(c_1, c_2, c_3, c_4) = (c_1, 5c_1, -c_1, -3c_1)##

They have taken the case that c_1 = -1, which gives their expression for a linear dependent function as they have shown. However, I'm confused that the functions are linearly dependent for any value of ##c_1 \in \mathbb{R}##. Since if we take ##c_1 = 0##, then ##c_1 = c_2 = c_3 = c_4 = 0##. I agree thought they the functions are linear dependent for ##c_1 \in \mathbb{R}\{0\} ## (Set of real numbers without zero)

Does someone please know why they did not include that case?

Thanks!

My solution is,

##(c_1, c_2, c_3, c_4) = (c_1, 5c_1, -c_1, -3c_1)##

They have taken the case that c_1 = -1, which gives their expression for a linear dependent function as they have shown. However, I'm confused that the functions are linearly dependent for any value of ##c_1 \in \mathbb{R}##. Since if we take ##c_1 = 0##, then ##c_1 = c_2 = c_3 = c_4 = 0##. I agree thought they the functions are linear dependent for ##c_1 \in \mathbb{R}\{0\} ## (Set of real numbers without zero)

Does someone please know why they did not include that case?

Thanks!