Ok, I think I understand. so that is linear because L(2,3,5) = (0,0). And L(ku) = kL(u) = (0,0).
But for b), the second part doesn't hold up because L(ku) = (1,2,-1) but kL(u) = k(1,2,-1) and they are not equal for all k.
and c probably shows something similar. I will have to write it out...
I guess my problem is, I don't know how to apply that to L(x,y,z) = (0,0). If it was L(v) = Av I would understand. I just don't understand the transformations themselves and how to apply them.
Homework Statement
which of the following are linear transformations.
a) L(x,y,z) = (0,0)
b) L(x,y,z) = (1 ,2, -1)
c) L(x,y,z) = (x^2 + y, y - z)
The Attempt at a Solution
I know that L is a linear transformation if L(u + v) = L(u) + L(v) and L(ku) = kL(u).
I am not sure how to...
I probably should have mentioned. I don't have the definition of the determinant to work with.
the problem actually says Show that the 2 x 2 matrix A is nonsingular if and only if ad-bc != 0.
I've figured out the If matrix A is nonsingular, then ab-bc != 0 side. I just need the if ad - bc !=...
Homework Statement
Prove: A 2x2 matrix is nonsingular if and only if the determinant != 0
The Attempt at a Solution
I need to prove this, using logic and maybe the theorem that a n x n matrix is nonsingular if and only if it is row equivalent to I_n.
I could use a push in the...
Homework Statement
Let L: R^3 -> R^3 be a linear transformation such that
L(i) = [1 2 -1], L(j) = [1 0 2] and L(k) = [1 1 3].
Find L([ 2 -1 3)].
All the numbers in [ ] should be vertical, but I don't know how to set that up.
Homework Equations
The Attempt at a Solution...
Homework Statement
Show that the following limit does not exist:
lim (x,y) --> (0,0) of x^2 / (y^2 + x^2)
Homework Equations
The Attempt at a Solution
I think it involves using l'hospitals rule and using partial derivatives, but I really don't know.
Homework Statement
Start with the power series representation 1/(1-x) = sum from n=0 to inf. of x^n for abs(x) < 1 to find a power series representation for f(x) and determine the radius of convergence.
f(x)=ln(5+x^2)
Homework Equations
The Attempt at a Solution
Okay, so I...
Homework Statement
Does this series converge or diverge?
Series from n=1 to infinity n(-3)^(n+1) / 4^(n-1)
Homework Equations
The Attempt at a Solution
Okay, I've tried it both ways.
Ratio test:
lim n --> inf. ((n+1)*(-3)^(n+1)/4^n) / (n * (-3)^n / 4^(n-1))
Now...
It's (1+sin(n)). Hrm, smaller than 2. So I can compare it to 1/5^n. Now, I need to figure out how to prove that series converges. Is it a geometric series?
Actually, I know it converges, based on the root test. But I don't think we can use the root test now.
Well, the top part diverges, the bottom causes it to go to 0. So I don't know what happens faster.
Either it converges to 0, or it diverges.
The solution must involve the comparison test or the limit comparison test. But I'm not sure what to compare it to.
Homework Statement
Does the sum of the series from n=1 to infinity of 1+sin(n)/10^n converge or diverge.
Homework Equations
The Attempt at a Solution
I can use the comparison test or the limit comparison test.
I'm not sure where to go from here.
the equation x sin (xy) +2x² defines y implicitly as a function of x. assuming the derivative y' exists, show that it satisfies the equation y'x² cos (xy) +xy cos(xy)+sin (xy)+4x = 0.
Help needed please.
I found the derivative of the first equation is:
sin xy + xy cos xy +4x. It's close...
of course I'm out on my differention. This text book is written in the most obscure way possible. I missed the lecture where we went over this. My head really hurts. I'm malnurished because college dining halls care more about being cheap than healthy.
And I'm supposed to be a physics major...
I don't understand it. How it works, etc...
I've read the book definition, looked it up on the internet, and I still don't get it.
Like the current problem I'm working on:
derivative of sin((cos x)^2)*cos((sin x)^2)