Which of the following defines an inner product on R^3 <(x,y,z),(a,b,c)>= xa+2xb+3xc <(x,y,z),(a,b,c)>= xy+za+bc <(x,y,z),(a,b,c)>= xa-yb+zC...
Which of the following is solution for (x^2 + y^2) dx +2xydy= 0? xy^2+1/3x^3=c x^2y+1/3x^3=c xy^2+1/2x^3=c x^2y+1/2x^3=c
12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal. 12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal.
32. Simplify : a. x/3-x/4 b. 3/(2x) -4/x c. 1/2x-1/3x 33. Find x if: 3x +6 = 2-5x a. b. x/m + x/n = 1 C 1/x = 3/m d. Sx/3 = 2 34. Find b if: x/(x+a) = 2/b a. b. v(x - b') =y 35. Solve the following Simultaneous linear equations and check in both equations: a) 3x+y=-4 x-2y 1 b) 5x+y=-8 2x-2y 4 Answer: x-1, y.3 36. Evaluate the expression below, if b-3 and c-2. 2bc'+(bc) Helpful...
3. Divergence Find the divergence of: a) Ē(x, y, z)=(-2y x 0] b) F(x,y,z)= (y2 – 2x 5x’y x+37] c) v =[3y–2yx xy? -62?x]
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
1. Solve the following differential equations: a. xy'=y+Vxy x+2y+3 y'= b. 2x – y +5 x+2y+3 y'= x+2y+5 y cos(x+y)+x+y d. sin(x + y) + y cos(x+y)+x+y C. y'=
a - e (a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.
#5 Determine for which values of the system 3x + 2y x + y +z = 2x + 2y + Az has: 4 p. a) one solution; 4 p. b) no solution. 4 p. c) infinitely many solutions;
Determine whether or not the field F (x,y,z) = (y4_47, 4x4°+62" - XZ, 12yz +10-xy) is conservative. If so, find (x, y, z), a Potential function for Be sure to check your answer! out Form om POP y-plane 20.) for both parts of this problem, the vector field is: < 2x + y, x-2y) & the corve is x=y² from er in din F(x,y) ..3 Do ad on A.) Compute F.Tds - Di de one of the following ways: See...