=== 3. For the vector field = -2zi-2y-2k, find the flux through the ellipsoids: (x²+12+12) (a) (-19)2 + (-18)2 + (8-17)² = 1 15 15 18 (b) (x+1)+(-2)²+(x+3)² = 1

Let B = matrix from B to C (B-{H·0] } ³ and C = be two bases for R². Find the change of coordinates

Let the vector C represents the coefficients of a polynomial pt=c1+c2t+c3t2+c4t3. Express the conditions p0=1, p'0=2, p1=1, p'1=0 in the form AC=b.

Let = [-5 1] and = [66]. Find the following vectors. v=5z ]. * - [ u=-6y= − [1 =52 – 6y = [ -

2.30 Let r denote a position vector r = x = xiêį (r² = x₂x₁) and A be an arbitrary constant vector. Use index notation to show that: (a) (c) ² (r) = n(n+1) rn-2. V. (rx A) = 0. (b) (d) V(r. A) = A. ▼x (rx A) = -2A.

What is the velocity​ vector?

Calculate the triple scalar products w. (v × u) and u ⋅ (w × v), where u = (7, 2, −1), v = w. (vx u) = 330 = (2, 8, -3), and w = u. (w x v) = 350 = (9, 8, -10).

Suppose the vector x characterizing the antigenic state of an influenza virus population changes from one season to the next according to the equation 23 Xt + 1 ¹ -[3.39]** 0 0.9 If the vector in the current season is [...] what was the vector in the previous influenza season? ↓ 1

#7

Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0), v̄=(5i+k) and w̄=(1,1,-2). Are they linearly dependent?