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  1. I'll denote dim(V) by n, and write B = {b_1... is a basis for V there are scalars c... is a basis for V, B is linearly independent...

    1 Answers · Science & Mathematics · 11/09/2013

  2. a) v(t) =-0.5(t+5)^2 +2000 v'(t) = -0.5 (2)(t+5) = -1(t+5) = -t-5 v'(10) = -10-5 =-15 (instantaneous...t)=-10 -10 = -t-5 add 5 to both sides -5 = -t t = 5 c) [v(2)-v(0)]/(2-0) = [v(2)-v(0)] /2 v(2) = -0.5(2+5)^2 +2000 = -0.5...

    1 Answers · Science & Mathematics · 02/09/2011

  3. v=√(9900/11) v=√900 v=+/-30

    4 Answers · Science & Mathematics · 27/09/2009

  4. v(t) = (t^7)^(1/2) - t^(1/2) v'(t) = 1/2(t^7)^(-1/2) * (7t^6) - (1/2)t^(-1/2) v'(t) = (7t^6)/2(t^7...

    2 Answers · Science & Mathematics · 14/10/2009

  5. If v has the same direction as u, it is a multiple of u. First we... u by √3, we can shorten it so that it's length is 2: v = u/√3 = (1, √3, 0) Hope this helps.

    2 Answers · Science & Mathematics · 20/05/2007

  6. v=-5i +6j W=-2i -3j now A.B = (mag.A)(mag.B)cos...in dot product, i.i = 1,j.j = 1 but i.j = 0 (as cos 0 = 1 and cos 90 = 0) hence, v.w = (-5i +6j)(-2i -3j) = +10i.i + 15i.j - 12j.i - 18j.j = +10 + 0 - 0 - 18 = 10 - 18...

    5 Answers · Science & Mathematics · 01/08/2007

  7. ... show that L^-1(T) is a subspace of V, we need to show three things: (1) The zero vector...we needed to prove. To prove (2), let u and v be in L^-1(T). Then we need to show...

    1 Answers · Science & Mathematics · 23/07/2012

  8. 195 = -v + 27 195-27 =-v 168 = -v v = -168.

    7 Answers · Science & Mathematics · 15/05/2010

  9. Let y = v z (where we use z instead of y1 for simplicity...39; = v ' z + v z' and y '' = v'' z + 2 v' z' + v z''... to u = (dv/dt) = 2k t^(-1/2) and so v = k t^(1/2) + C and therefore y = v z...

    1 Answers · Science & Mathematics · 19/07/2012

  10. Suppose that u,v is linearly independent but not spanning. Since they are... not spanning, there is a vector w so that a_1*u + a_2*v ≠ w for any choice of a_1 and a_2. Now, suppose that u,v,w are...

    2 Answers · Science & Mathematics · 29/04/2013

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