At 3:39, am unclear what is meant by "is the zero function" (at least thats what i'm hearing in your narration) after you've said that we're not interested in only one value of x since the equation will equal zero at a particular value (and appropriate multiples of it) of x and allowing the scalars to be equal (or it could also be done w different value of x and appropriate values of the scalars).
For "sin x" and "cos x" to be linearly independent *functions*, there would have to be values of u1 and u2 for which u1 sin x + u2 cos x equals the zero function (which is zero no matter what you plug in for x). It wouldn't be enough for u1 sin x + u2 cos x to equal zero for some particular value of x.
great video, really helpful!
Keep it going, man!
At 3:39, am unclear what is meant by "is the zero function" (at least thats what i'm hearing in your narration) after you've said that we're not interested in only one value of x since the equation will equal zero at a particular value (and appropriate multiples of it) of x and allowing the scalars to be equal (or it could also be done w different value of x and appropriate values of the scalars).
For "sin x" and "cos x" to be linearly independent *functions*, there would have to be values of u1 and u2 for which u1 sin x + u2 cos x equals the zero function (which is zero no matter what you plug in for x). It wouldn't be enough for u1 sin x + u2 cos x to equal zero for some particular value of x.
@@HamblinMath Got it, thanks.
Thank you so much