Question

Show that the pair of equations A = 1/2 ( B × r) , B = ∇ × A is satisfied by any constant magnetic induction B.

Answer #1

Show that for all a; b; c 2 R the following system of equations
is consistent
x + 2y + z = a
x + 3y + 3z = b
x + 4y + 2z = c

Solve the following pair of simultaneous equations for x and y.
qx+ (1− p)y = R and px+ (1−q)y = S.

Problem
1. Starting with the defining equations for R and C, show that
RC has units of time.
2. Starting with the defining equations for L, R, and C, show that
wL and 1/ wC both have units of ohms.
3. Show that taking the time derivative of any sinusoidal function,
such as cos ( wt +phi ), has the effect of advancing its phase by
pi/2.
4. If the internal resistance of an inductor is not negligible, how
does...

slext the correct equations that show that the calie of the Rydberg
constant is R =1.0974*10^7 m^_1.Evaluate R using tge Bohr
model.compare the following equation
1/wavelength=R(1/2^2-1/n^2),n=3,4.... and
1/wavelength=2pi^2z^2e^4mk^2/h^3c(2/n'^2-1/n'2)at Z=1

Graph Theory
Using proof of induction and Ramsey's Theorem, show
R(3,t) ≤1+2+3+...+t for each t≥2.

(a) If r^2 < 2 and s^2 < 2, show that rs < 2.
(b) If a rational t < 2, show that t = rs for some rational
r, s with r^2 < 2, s^2 < 2.
(c) Why do (a) and (b) show that that √2 * √2 = 2?

Determine if the ordered pair is a solution to the system of
equations.
y=-1/2x-1
3x-2y=13
a) Is (2,-2) a solution to the system of equation. yes or
no.
B) Is (-4,1) a solution to the system of equation yes or no.

3. (a) Consider R 3 over R. Show that the vectors (1,
2, 3) and (3, 2, 1) are linearly independent. Explain why they do
not form a basis for R 3 .
(b) Consider R 2 over R. Show that the vectors (1, 2),
(1, 3) and (1, 4) span R 2 . Explain why they do not form a basis
for R 2 .

1) Solve the system of equations. Give your answer as an
ordered pair (x,y)
{y=−7
{5x-6y=72
a) One solution:
b) No solution
c) Infinite number of solutions
2) Solve the system of equations. Give your answer as an
ordered pair (x,y)
{x=2
{3x-6y=-30
a) One solution:
b) No solution
c) Infinite number of solutions

1.
Suppose that ? is a finite dimensional vector space over R. Show
that if ???(? ) is odd, then every ? ∈ L(? ) has an eigenvalue.
(Hint: use induction).
(please provide a detailed proof)
2. Suppose that ? is a finite dimensional vector space over R
and ? ∈ L(? ) has no eigenvalues. Prove that every ? -invariant
subspace of ? has even dimension.

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