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1. ### PROOFS! Help Please!!! Suppose T: U→V and S: V→W are linear transformations...?

... x is in V and T is onto then we can find u in U such that T(u)=x. Applying S on both sides...

2 Answers · Science & Mathematics · 31/10/2012

2. ### Find an inverse mapping for (u,v) = F(x,y) = (y + xy, y - xy)?

u = y + xy v = y - xy Add u + v: u + v = 2y y = (u + v) / 2 Subtract u - v: u - v = y + xy - (y - xy) u - v = xy + xy u - v = 2xy x = (u - v) / 2y x = (u - v) / (u + v) Answer: x = (u - v) / (u + v) y = (u + v) / 2

3 Answers · Science & Mathematics · 24/11/2015

3. ### If u=kv, where k is a real number and u and v are vectors, state 3 true statements about u and v?

u and v are parallel u.v = |u||v| u x v = 0 (Cross product) Note they do not necessarily lie on the same plane or line, all we can say is that they have the same direction.

4 Answers · Science & Mathematics · 29/06/2010

4. ### Mathematics integrals question R(u,v) notation?

...of sine and cosine. [More explicitly, the rational function is R(u, v) = v/(u + uv). So, R(sin x, cos x) = cos x/(sin x + sin x cos x...

1 Answers · Science & Mathematics · 01/04/2012

5. ### Find the integral of x/(2x+1) ???????? --(u substitution i think)?

Hello, ∫ [x /(2x + 1)] dx = let: 2x + 1 = u 2x = u - 1 x = (1/2)(u - 1) dx = (1/2) du then, substituting...u) du = (1/4)u - (1/4) ln | u | + C let's substitute back 2x + 1 for u: (1/4)(2x + 1) - (1/4) ln |2x + 1| + C = (1/2)x + (1/2) - (1/4) ln |2x...

1 Answers · Science & Mathematics · 01/03/2013

6. ### Let U=span{(1,-2,0,1),(1,-2,1,0)}, a subspace of R^4?

...attempt submitted whilst non compos mentis (a) If u=(u1,u2,u3,u4) ∈ U┴ then u is perp to both spanning... to u2=1/11, u4=8/11 ∴ p−w belongs to U

1 Answers · Science & Mathematics · 11/04/2012

7. ### ||u||=3, ||v||=5, ||3u + v|| = 10, find the angle between u and v? vectors?

...3u|^2 + |v|^2 - 2|3u||v|cosθ, where θ is the angle between 3u (and, thus, u) and v. Since |3u| = 3|u|, we have: |3u + v|^2 = (3|u|)^2 + |v|^2 - 2(3...

2 Answers · Science & Mathematics · 12/09/2012

8. ### Let (a_n) from (n=1 to∞) be a sequence in R^k with lim a_n = a. Show that {a_n: n≥1} U {a} is closed.?

Let X = {a_n: n ≥ 1} U {a}. Suppose x ∈ R^k \ X. Then x ≠ a and x...

2 Answers · Science & Mathematics · 28/11/2013

9. ### If U and W are subspaces of V, prove that (U+W)\W is isomorphic to U\(U intersects W)?

Consider the linear transformation F : U → (U + W)/W given by F...v in U : v is in W} .........= U ∩ W. The result now follows from...

2 Answers · Science & Mathematics · 17/03/2012

10. ### given u = 2vx^2, how can i use ln and turn it into linear equation? so far i have this?

ln u = ln (2vx²) ln u = ln (2v) + ln (x²) ln u = ln (2v) + 2 ⋅ ln (x) If you allow for a little substitution: y = 2⋅x + ln...

3 Answers · Science & Mathematics · 19/10/2007