Inverse Definition and 1000 Threads

Homework Statement see attachment Homework Equations The Attempt at a Solution I don't get the part where it says "Solving this equation for X(s), we obtain ..." Specifically jumping from 3/s(s2+3s+5) to (3/5)(1/s)-(3/5)[(s+2)/(s2+2s+5)]. How did the problem break up this...

This is problem 4.14 in Advanced Calculus of Several Variables. Two questions: Is my proof correct? And: is there a cleaner way to prove this? Show that, if ad = bc , then the matrix \left [ \begin{array}{cc} a & b \\ c & d \\ \end{array} \right] has no inverse. My attempt: Suppose there is...

If we see the form \sqrt { { a }^{ 2 }-{ x }^{ 2 } }, we always set x=asinθ How do we know that it will work in advance? Just trial & error?

Homework Statement Find the computational cost for finding the inverse of an nxn matrix via Gauss-Jordan elimination. That is setting up A|I and converting it to I|A-1.Homework Equations The Attempt at a Solution So I can't see where I went wrong, but my answer does not agree with my fellow...

Homework Statement The matrix given is row 1: [0,1] row 2: [1,0] The matrix above if you switch row 1 with row 2 is just the identity matrix. So wouldn't that matrix already be the inverse of the identity matrix? Homework Equations The Attempt at a Solution

Homework Statement Prove that the inverse of a bijective function is also bijective. Homework Equations One to One f(x_{1}) = f(x_{2}) \Leftrightarrow x_{1}=x_{2} Onto \forall y \in Y \exists x \in X \mid f:X \Rightarrow Y y = f(x) The Attempt at a Solution It...

Is this sufficient?

Homework Statement a)Use Gauss-Jordan elimination to find the inverse of A = [ 2 1 4 ] [ 1 1 2 ] [ -2 -3 -2 ] b) Use the result from part a) to find the solution of the following system. 5x+2y-3z = 5 x+y-z = -1 -3x-y+2z = 2 Homework Equations The Attempt...

Sorry for the poorly-worded title. I help tutor kids with pre-calculus, and they're working inverse functions now. They use the "horizontal line test" to see if a function will have an inverse or not by seeing visually if it's one-to-one. I was thinking about what that might imply. If a...

I'm applying laplace transform to a spring-mass system, the most basic one. I write this code which takes initial values x(0) and v(0) as input and I'm computing x(t) in matlab. But for some values it gives me complex roots for x(t) which doesn't seem possible. If not for laplace I can solve the...

Hi, I've a very trivial numerical problem where I'm currently stuck. In MATLAB the matrix Hf: >> Hf Hf = 1.0e+003 * 1.6443 1.6516 1.6583 4.8373 4.8349 4.8334 4.6385 4.6418 4.6445 -9.6014 -9.6084 -9.6154 And the following vectors which...

Homework Statement If cos^{-1}\frac{x}{a}+cos^{-1}\frac{y}{b} = \alpha then show that \frac{x^2}{a^2}-\frac{2xy}{ab}cos \alpha + \frac{y^2}{b^2} = sin^2 \alpha Homework Equations The Attempt at a Solution I assume inverse functions to be θ and β respectively. So in the second equation...

In this video: At the time 2:10, I don't understand why we have to note that \lambda^3 - 8\lambda and \lambda^2 + 1 are relatively prime. Thanks in advance

Homework Statement Solve cot^{-1} x - cot^{-1} (n^2 - x+1)=cot^-1(n-1) Homework Equations The Attempt at a Solution I can write the above equation as θ+α=β where the symbols represent the respective inverse functions. Now I take tan of both sides. Simplifying I get...

Homework Statement Let A\inM_{n}(\Re) a matrix verifying A^{3}-A^{2}-I_{n}=0 a) Show that A is inversible and calculate it b) Show that the solution X\subsetM_{n}(\Re) of the equation A^{k}(A-I_{n})X=I_{n} has a unique solution. The Attempt at a Solution I'm having...

Homework Statement What is the inverse of this logarithm equation? y=-log5(-x) i tried it and i got y=-5(-x)hm.. you know how people say that if you want to find the inverse graph of something just switch the x and y coordinates from the table of values? Well i also tried that approach and...

Hello I need some help proving the next thing, I can't seem to be able to work it out.. Let A be an nxn matrix. Prove that: (adj A)^{-1} = adj(A^{-1}) Thanks...

Homework Statement Say we have a 2D rigid body transform, with parameters p = [ p_1,p_2,p_3] for rotation, x translation and y translation respectively. I'm using the transform to .. transform an image. Is there a way to have: For a point x , y : x',y' = transform(x,y,p) <=> x,y =...

Homework Statement What is the inverse laplace transform of (1/(s+s^3))? Homework Equations The Attempt at a Solution I looked it up on wolframalpha and got 1-cos(t), but I don't understand how they got that answer. I looked up a basic laplace transform chart and didn't see anything...

Homework Statement Assume that the Derivative Rule for Inverses holds. Given that f(x) = x + f(x), and g(t) = f-1(t), which of the following is equivalent to g'(t)? a. g'(t) = 1 + t2 b. g'(t) = 1 + t4 c. g'(t) = 1 + g(x) d. g'(t) = 1 / (1 + t4) Homework Equations The Attempt at a...

Homework Statement Find inverse Laplace transform \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]Homework Equations The Attempt at a Solution I try with theorem \mathcal{L}[f(t)*g(t)]=F(s)G(s) So this is some multiple of \mathcal{L}[\sin at*\sin at] So \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]=\propto...

Hi I'm reading a book called Calculus lifesaver, and in the book they state that the inverse of a function f(x)= x3 is the same as f-1(x)=3√x and is the same as f-1(y)=3√y So I did a test, with a simpler function and I can't see how this is true If I have a function f(x)= 2*x Then...

Homework Statement Given f(x) = x2+3x+2, what is f-1(f(x))? Homework Equations The Attempt at a Solution Algebraically, getting f-1(x) is as follows: y=x2+3x+2 x=y2+3x+2 y=+/-√(x+0.25)-1.5 f-1(x)=+/-√(x+0.25)-1.5 f-1(f(x))=+/-√(x2+3x+2+0.25)-1.5...

Hello, let's suppose I have two functions \phi:U\rightarrow V, and T:V\rightarrow V that are both diffeomorphisms having inverse. Furthermore T is linear. I consider the function f(u) = (\phi^{-1}\circ T \circ \phi)(u), where \circ is the composition of functions. Since T is linear, we...

Homework Statement Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous. Homework Equations I have no idea. The Attempt at a Solution I seriously have no idea. This is for my analysis course, and I'm not...

Hi, If A is some nonsquare matrix that is possible rank-deficient, then am I right to understand that (A^T)(A) is a positive semidefinite matrix? Does there exist an inverse (A^T A)^-1? Thanks for any help

Is $F^{-1}(F(E))\cap E=E$? Thanks!

Homework Statement Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities: Homework Equations Here are the given identities: The Attempt at a Solution Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this...

This is a conceptual question on the region of convergence (ROC) and the inverse Laplace transform (ILT). Here the bilateral laplace transform (LT) and the ILT are given by F(s)=L\{f(t)\}=\int_{-\infty}^{+\infty} f(t) e^{-st} dt and f(t)=L^{-1}\{F(s)\}=\frac{1}{i...

Homework Statement Find the inverse function of y= x/2 - 5/2x Homework Equations The Attempt at a Solution I've tried to manipulate the equation to find x(y) without any sucsses.

Homework Statement For a physics problem I must take the inverse Fourier transform of 2 functions. Namely I must compute the integral ##\frac{1}{\sqrt{2\pi}}\int_{-\infty} ^\infty [A\cos (ckt)+B\sin (ckt)]e^{ikx}dk##.Homework Equations Already given. i is the complex number. t is greater or...

Homework Statement Find (X * Y-1)T - (Y * X-1)T When X = [3 5] .....[1 2] and Y = [3 4] ...[2 3] Homework Equations Inverse= 1/ad-bc [d -b] ......[-c a] The Attempt at a Solution I got: [9 -6 ] [14 -9] But the answer is: [-3 -2] [6 3]I did the problem twice and got the same answer so I...

Finding the inverse of a function? Homework Statement Find (f^-1)'(a), a =2 √(x^3 + x^2 +x +1) So, if a = 2, then f^-1(2) = 1 and f(1) = 2 Homework Equations The Attempt at a Solution I figured out that f(1) = 2, so √(3(1)^2 + 2(1) + 1) = √6 so the...

Hello, This is not a homework exercise, so I decided to post it here. Hopefully one of you could help. I would like to find an explicit expression for (I-A)^(-1), provided that A is a squared matrix (nxn) and A^k = 0. It is also given that I-A^k = (I-A)(I+A+A^2+...+A^(k-1)). I understand that by...

For any A \in \mathcal{R}^{n \times m}, does A^T A have an inverse? From the wikipedia article for transpose ( http://en.wikipedia.org/wiki/Transpose ), I found that A^T A is positive semi-definite (which means for any x which is a column vector, x^T A^T A x \ge 0 ). And the Wikipedia article...

I tried posting this at stack exchange but it never got the question answered. I want to prove this: If f:U→C is holomorphic in U and invertible, P∈U and if D(P,r) is a sufficently small disc about P, then f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds

Hello, Would it be correct to say that if for every two different vectors x and y, A*x ≠ A*y (where A is a symmetrical matrix), then A is NOT necessarily invertible? In other words, albeit for any two different vectors x and y symmetrical matrix A times one of the vectors is not equal to A...

Hello everyone! I have three questions: (1) If $x\in R$, is it true that $f ^{-1} (f(x)) = x$? (2) If $y\in R$, is it true that $f (f^{-1}(y)) = y$? (3) If $B\subset R$, is it true that $f(f ^{-1} (B)$? I think I have showed it for (3), but not sure of my proof. For (1) and (2), I considered...

I am currently doing a trig question and trying to find the location of the acute angles of cosine inverse and I am just wondering if cosine inverse follow the cast rule? In other words would it be positive where cos would be positive or not?

Hi, all I am looking into inverse cosine operations. I have a question like follows: Let x and y be two variables of degrees, how to separate equation arccos(x+y) into an equation that contains x and y separately? Such as arccos(x+y) = f1(...x) + f2(...y)? Thank you very much for your...

The Title pretty much says it all. I'm trying to learn how to solve the Inverse Laplace Transformation of Arctan(s/2). An equation of this sort was not explicitly covered in class and I'm having difficulty figuring where to start to solve it. If anyone could give me a general idea that would...

Hi Does anyone know if there is a relation between the Fourier transform of a function and the Fourier transform of the inverse function in summary FT[f(x)] ?= FT[f-1(x)] Thanks!

Homework Statement There were other questions before this one but i solved them all. Find the inverse function of f(x)=arctan(\sqrt{1+x^{2}}-x) for every x in the interval ]0,pi/2[ .That's the interval that I found when counting f(R) because f is a bijection from R to f(R). Hence...

Homework Statement How to solve part (iv) & (v)Homework Equations general form : y = a(x-h)^2 + kThe Attempt at a Solution In part (iv) for finding domain and range I converted g(x) in general form and then compared it with general form.

Treatment originally used to discard inverse square law as solution to Olbers' paradox was not set up correctly. If we include sensor (camera) in the treatment and model light as photons the result describes what we actually see.

Homework Statement I need to expand 1/y(x)2 , where y(x)=x1/2Ʃ(-1)n/(n!)2 * (3x/4)n for n=0 to ∞ Homework Equations How does one arrive at the correct solution (-coefficients seem to vanish, only + remain)? The Attempt at a Solution I know that x1/2Ʃ(-1)n/(n!)2 * (3x/4)n expands...

I can't seem to make head or tail of the description of direct and inverse limits of abelian groups in problems 8 and 10 of the attached excerpt from Dummitt and Foote. Does anyone have a simpler or more intuitive definition of these two notions, or just an explanation of Dummit and Foote's...

Homework Statement This is a practice problem for a test on Laplace transforms Find L^-1[ (9s^3+17s^2+66s+45) / (s^2+9)(s+2)^2 ] (L^-1 = inverse laplace transform) Homework Equations From Laplace transform tables: L^-1[ 1 / s-α ] = e^αt L^-1[ s / s^2+ω^2 ] = cos(ωt)...

Homework Statement Assume the function f defined by f(x)=5x+sin(πx) is strictly increasing on ℝ. Find (f^{-1})'(10) Homework Equations Let I and J be be intervals and let f:I->J be a continuous, strictly monotone function. If f is differentiable at c and if f'(c)≠0, then (f^{-1}) is...

Does inverse square law apply to light in vacuum?