# Stanford University Derivatives Problems Analysis Real Analysis proof, Need the strict proof of these real analysis question. Thank you a 10.1. In lecture

Stanford University Derivatives Problems Analysis Real Analysis proof, Need the strict proof of these real analysis question. Thank you a

10.1. In lecture I explained that the expansion of the determinant of a matrix A has a term for every

transversal of A, which is either added or subtracted depending on the choice of transversal.

I also said that if some of the entries of A vanish, then some of the transversals do too, and

those can be skipped in the expansion of detA. Let a,b+0), and let A be an n x n matrix

with a on the diagonal, with b just above the diagonal, and with b in the lower left corner,

like this:

[a b 0 0]

[a b 0 0 0]

0 а ь о 0

0 a b 0

| oo a bo

oo a b

000 a b

b 0 0 a

b 0 0 0

Describe the non-zero transversals of A and find detA.

10.2. Spherical coordinates for R}, minus the z axis, are defined by:

(x,y,z) = (r, 0,0) = (r(sin )(coso), r(sin ) (sin o), r(cos O)).

Find the Jacobian matrix Dg for this coordinate system. As in problem 10.1, list the terms

in the transversal expansion of det Dg, skipping the terms that are always zero. Also calcu-

late absolute Jacobian determinant to obtain the volume element for spherical coordinates,

simplified as much as possible. (Hint: The determinant simplifies with repeated use of

sin? +cos= 1.)

10.3. Let X CR2 be the union of these two parametric curves:

(x,y) = g(t) =(t, sin(3/t))

t>O

(x,y)=h(t) = (0,1)

t

Purchase answer to see full

attachment

## We've got everything to become your favourite writing service

### Money back guarantee

Your money is safe. Even if we fail to satisfy your expectations, you can always request a refund and get your money back.

### Confidentiality

We don’t share your private information with anyone. What happens on our website stays on our website.

### Our service is legit

We provide you with a sample paper on the topic you need, and this kind of academic assistance is perfectly legitimate.

### Get a plagiarism-free paper

We check every paper with our plagiarism-detection software, so you get a unique paper written for your particular purposes.

### We can help with urgent tasks

Need a paper tomorrow? We can write it even while you’re sleeping. Place an order now and get your paper in 8 hours.

### Pay a fair price

Our prices depend on urgency. If you want a cheap essay, place your order in advance. Our prices start from $11 per page.