Homework Statement
I'm doing a physics lab and have a question about RC circuits. I'm given four formulas:
1a) dQ/dt = -Q/RC
1b) Q = (Qo)e^(-t/RC)
1c) E - RI - Q/C = 0 ---> R(dQ/dt) + Q/C - E = 0
1d) Q(t) = CE[1 - e^(-t/RC)]
I am told that 1b is the solution to 1a and 1d is the...
Homework Statement
Give a proof by Mathematical Induction of the following:
For all integers n>=3, (n^2 - 3n + 2) is positive.
Homework Equations
The Attempt at a Solution
Hey guys, this is a problem from my discrete mathematics study guide. Here's what I got so far:
Proof: n-initial=3...
Homework Statement
Let V be the subspace spanned by the following vectors:
[ 0]...[ 1 ]...[2]
[ 2]...[ 1 ]...[5]
[-1]...[3/4]...[0]
Determine a basis for V.
The Attempt at a Solution
I'm not quite sure how to start here. Would placing the vectors in a matrix and deriving its...
How do I derive the elements of my set from the equation?
If I select a0=2, a1=3, a2=4, and a3=6, then these numbers meet the requirements of the equation.
Similarly, a0=-2, a1=-3, a2=-4 and a3=-6 would as well. Where do I go from there?
Homework Statement
Is {a0 + a1x + a2x^2 + a3x^3 | a0a3 - a1a2 = 0} a subspace of P3? Why or why not?
*The digits should be in subscript.
How would I go about answering this?
I think I've actually got this figured out. I just test two 2x2 matrices of random values under the various axioms and if they pass then under matrix addition and scalar multiplication then it should show that all 2x2 matrices are a real vector space right?
What other kind of vector space is...
Homework Statement
Show that all 2 x 2 matrices with real entries:
M(2x2) = {
a b | a,b,c,d are real numbers}
c d |
is a vector space under the matrix addition:
|a1 b1| + | a2 b2| = |a1+a2 b1+b2|
|c1 d1| + | c2 d2| = |c1+c2 d1+d2|
and scalar multiplication:
r*| a b | = | ra...
Homework Statement
Two point charges -2Q and +3Q are on the x-axis at the origin and at
x = L. Find all the points on the x-axis (not at infinity) where the electric
potential is zero. Express your answers in terms of L and Q.
Homework Equations
V= k*Q/r
The Attempt at a Solution
I...