# Recent content by lkh1986

1. ### Column Space of Matrix A and ref(A)

Homework Statement Given a matrix A. So I can reduce A to ref(A). Let's say in ref(A), the columns that contain leading ones are column 1, 3, and 5. True or false: (a) Columns 1, 3, and 5 from ref(A) form the column space of ref(A). (b) The corresponding column 1, 3, and 5 from the original...
2. ### Derive the Integrating Factor for Homogeneous DE

Homework Statement I have this statement: If M(x,y)dx+N(x,y)dy=0 is a homogeneous DE, then μ(x,y)=\frac{1}{xM+yN} is its integrating factor. The problem is, how do we derive this integrating factor? Homework Equations For homogeneous DE, we have f(kx,ky)=k^n*f(x,y) We also have...
3. ### Distance to the corner of a rectangle

Since the question says d is an integer, I try to use other types of 'combination', and when I tried with '6, 9, 7, d' going clockwise, I get d = 2. Yay! Thanks again, eumyang, for the help :)
4. ### Distance to the corner of a rectangle

Yup. I should have used the "6, 7, 9, d" clockwise. I recount, and get √68. :) EDIT: No diagram was given for the question.
5. ### Distance to the corner of a rectangle

v_{1}^{2}+h_{1}^{2}=6^2=36 v_{1}^{2}+h_{2}^{2}=7^2=49 v_{2}^{2}+h_{1}^{2}=9^2=81 v_{2}^{2}+h_{2}^{2}=d^2 d^2=v{2}^{2}+h_{2}^{2}=130-36=94
6. ### Distance to the corner of a rectangle

Thanks for the clue. Now I have a clearer direction. I get d = √94, not an integer though, but still, at least I can get the value of d. :)
7. ### Distance to the corner of a rectangle

Homework Statement This question is taken from 2011 Malaysian Mathematical Olympiad. Mary is standing in a rectangular garden. Her distance to the four corners of the garden are 6 m, 7 m, 9 m and d m, respectively, where d is an integer. Find d. Homework Equations Triangle...
8. ### Find the limit

Can I use the series expansion? \frac{sin^{-1}x}{x} =\frac{x+\frac{X^3}{6}+\frac{3x^5}{40}+...}{x} =1+\frac{x^2}{6}+\frac{3x^4}{40}+... Then I can get limit = 1 when I substitute x = 0. Can we get the same answer without using the series expansion thingy?
9. ### Find the limit

Another question: Find the limit of \frac{sin^{-1}x}{x} when x approaches 0. The answer given is 1. Seems like I can't express arcsin explicitly. Any clue on how to start? :)
10. ### Find the limit

Yay, I get it. I multiply by another conjugate and eventually the (2-x) term will cancel out. Then I will get 2/4 which is equal to 1/2. Thanks so much for the help. :) \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} =\frac{(\sqrt{6-x}-2)(\sqrt{3-x}+1)}{(\sqrt{3-x}-1))(\sqrt{3-x}+1)}...
11. ### Find the limit

Oops, sorry. Now I have \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} =\frac{(\sqrt{6-x}-2)(\sqrt{3-x}+1)}{(\sqrt{3-x}-1))(\sqrt{3-x}+1)} =\frac{(\sqrt{6-x}-2)(\sqrt{3-x}+1)}{2-x}
12. ### Find the limit

Homework Statement Find the lim of \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}when x approaches 2, without using L'hopital rule or the definition. Homework Equations The Attempt at a Solution I try to multiply both the numerator and the denominator to get \frac{(\sqrt{6-x}-2)(\sqrt{3-x}-1)}{2-x}...
13. ### System of Linear Equations - Proving

Homework Statement Given that the values for a, b, c, d, e and f for the system ax+by=e, cx+dy=f has two different solutions. Show that ax+by=0, cx+dy=0 also has two different solutions. Homework Equations The Attempt at a Solution There're three cases of how two straight lines...
14. ### MATLAB Neural Network Classification Problem

Homework Statement P = [data(1:65,11:100) data(1:65,411:500)]; % Input, all together 180 data set, 65 dimension T = [ones(1,90) zeros(1,90); zeros(1,90) ones(1,90)]; % Actual output, first 90 data set belong to class I and the next 90 belong to class II net =...
15. ### Differences between Two Notations in DE

Homework Statement Is there any difference between the two notations below? Or can they be used interchangeably? \tilde{x} and \underline{x} (not an underline, but the tilde is at the bottom of the unknown x) Homework Equations The Attempt at a Solution From my observation...