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Doh! I forgot the middle rectangular prism will also be (obviously) shrinking. I re-did the exercise and got the right answer. Thank you very much Dr. Peterson

From this site: https://www.whitman.edu/mathematics/calculus_online/section06.02.html Exercise 6.2.13: The trough shown in figure 6.2.6 is constructed by fastening together three slabs of wood of dimensions 10 ft × 1 ft, and then attaching the construction to a wooden wall at each end. The...

Romsek, HallsofIvy, topsquark, and Subhotosh Khan, 1. Substituting x^2 + y^2 for r^2 worked perfectly and I got zero so thank you for that hint. 2. Thank you also for pointing out my spelling error which is quite embarrassing as not an error I should have made. Sorry about that. 3. Regarding...

Hello All, This is from http://math.mit.edu/~jorloff/suppnotes/suppnotes02/v6.pdf F = -y/(r^2) î + x/(r^2) ĵ Page says curl F = 0 and cites a previous example. ....... sp. edited I cannot find the sited previous example But I get curl F = 1/(r^2) - -1/(r^2) = 2/(r^2) I cannot figure out what...

Hello pka, Your concerns are totally justified. I have no background in field theory or Abelian group theory. I am just an old math hobbyist learning for fun from textbooks with no formal education or classes. My current Linear Algebra library includes Hefferon, Axler, Lay, Anton, and Strang. I...

Hello Everyone, I've been given an explanation. The "over" refers to the field in which the scalar multipliers are in. So a vector space over R means the scalar multipliers are always real numbers. The components of the vectors don't need to be in the field. They just need to be components of...

Hello All, I’m reading Axler “Linear Algebra Done Right” I’m still very much a beginner in linear algebra. My other linear algebra sources all only teach, at least so far, using just Real numbers. Axler uses both Real and Complex numbers, using symbols R, C, and F where F is all of both real...

Makes total sense. Thank you.

Hello, On this page - http://www.math.umbc.edu/~campbell/Math221/Glossary/ This definition: Codomain The codomain of a linear transformation is the vector space which contains the vectors resulting from the transformation's action. Thus, if T(v) = w, then v is a vector in the domain and w is...

Aha! That's it! 1/2 x = sin u dx = 2 cos u du I missed that now the 2 is back in there. So it's 2 arcsin (x/2) (not just arcsin (x/2)) Thank you very much!

Exercise: Integral from 0 to 1 of 2/((4-x^2)^(1/2)) or 2/sqrt(4-x^2) Book pulls out the 2 in the numerator and calculates arcsin(x/2) from 0 to 1 = pi/6. Then multiplies by the 2 for a final answer of pi/3. I factored out the 4 under the radical which becomes 2 in the denominator which cancels...

Hello All, Can ignore this. I was able to confirm answers to all 3 questions are all "yes". Thank you

Hello All, Given: f : R3→R r : R→ R3represents position of moving object as a function of time g(t) is valueof f at the object’s position at time t Firstquestion: Is all thiscorrect for me to say: w = f(x,y,z)= f(r(t)) = g(t) Secondquestion: Are partialderivatives of w and of f the...

Aha, I think this is what you meant for me to do. ln│csc x – cot x │ = - ln│1 / (csc x – cot x) │ = - ln│(csc x + cot x) / ((csc x)^2 – (cot x)^2) │ = - ln│(csc x + cot x) / ((cot x)^2+1 – (cot x)^2) │ = - ln│(csc x + cot x) │ Thank you very much stapel, I would not have gotten thiswithout...

When I evaluated ∫ csc x dx, I used csc x – cot x for mysubstitution instead of csc x + cot x So my final answer is ln│csc x – cot x │ + C The correct answer is -ln│csc x + cot x │ + C My answer seems to also be correct but I cannot prove it sonot sure what I’m missing. Any insight greatly...

Great, thank you.

HelloAll, Thisis from the document found here: https://math.dartmouth.edu/archive/m12f10/public_html/RepresentingMatrix.pdf (7) (Very importantexample) Let A be any m x n matrix. Then A defines alinear map LA : Rn →Rm (“left-multiplicationby A”) defined by LA(v) = Av for v ϵ Rn. Note that...

Hello Everyone, Wow, I apologize as I feel like I created a firestorm here and that was not my intent. I'll try to clarify everything here. My question came from Exercise 4.20 (e) on page 135 of the book PDF (Chapter 2 (Vector Spaces), Section III.4 (Basis and Dimension . Combining Subspaces)...

Hello Everyone, Sorry for the long delay but I wanted to get this figured out before replying. I have confirmed definitely this is a subspace and the book is wrong. Thank you all very much for all your assistance.

Yes, scalars are in R. Also, I am very aware that I don't know what the heck I'm doing so if my question is too incoherent to answer, just let me know and I'll carry on until I am knowledgeable enough to ask a lucid question. Thank you