u =<4, -5 > v=<3, 2 > | 2u – vl = ? Whole number. <7, -1, 5 >.< 2, 3, 1>=? whole number
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
3. (6 marks) Suppose that u, v and w are vectors in R3, and that u. (v x w) = 3. Determine (a) u (w x v) (b) u: (w X w) (c) (2u x v). w
(6 marks) Suppose that u, v and w are vectors in R 3 , and that u · (v × w) = 3. Determine 3. (6 marks) Suppose that u, v and w are vectors in R3, and that u. (vx w) = 3. Determine (a) u (w xv) (b) u (w xw) (c) (2u xv).w
NEED SOON: Find the image of the set S under the given transformation. S = {(u, v) | 0 ≤ u ≤ 4, 0 ≤ v ≤ 3}; x = 2u + 3v, y = u − v
u and v are perpendicular. Find the triple scalar product of u, v and w=-3⋅u×v+2⋅u+6⋅v if |u|=6, |v|=8.
(1 point) Solve the heat problem with non-homogeneous boundary conditions ∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0 u(0,t)=0, u(3,t)=2, t>0,u(0,t)=0, u(3,t)=2, t>0, u(x,0)=23x, 0<x<3.u(x,0)=23x, 0<x<3. Recall that we find h(x)h(x), set v(x,t)=u(x,t)−h(x)v(x,t)=u(x,t)−h(x), solve a heat problem for v(x,t)v(x,t) and write u(x,t)=v(x,t)+h(x)u(x,t)=v(x,t)+h(x). Find h(x)h(x) h(x)=h(x)= The solution u(x,t)u(x,t) can be written as u(x,t)=h(x)+v(x,t),u(x,t)=h(x)+v(x,t), where v(x,t)=∑n=1∞aneλntϕn(x)v(x,t)=∑n=1∞aneλntϕn(x) v(x,t)=∑n=1∞v(x,t)=∑n=1∞ Finally, find limt→∞u(x,t)=limt→∞u(x,t)= Please show all work. (1 point) Solve the heat problem with non-homogeneous boundary conditions au ди (x, t) at (2, t), 0<x<3, t> 0 ar2 u(0,t) = 0, u(3, t) = 2, t>0, u(t,0)...
Caculate w=2U+V, |U|,|V| and |W| A= <1,-3,7> and B=<-5,2,-3> Find C sp A+B+C=0
(6 marks) Suppose that u, v and w are vectors in R3, and that u. (v x w) = 3. Determine (a) u (w xv) (b) u. (w xw) (c) (2u x v). w
Im In F 1 1 Re -6 -5 -4 -3 -2 -1 -it N 3 4 5 6 LL -6 -5 -4 -3 -2 Im Im ih -6-5-4-3-2 2 -it 5 Re 6 -6 -5 -4 -3 -1 -il Find the modulus r. o Graph the complex number. 2 + Si Im Im iF Re -6 -5 -4 -3 -2 -1 -i 1 2. 3 4 5 6 -6-5-4-3 -2 -1 -F 1 2 3 Im Im -6-5-4-3-2-1 - 1...