Find ||u||, ||v||, and ||u + v||. (1, -2, 0, 2), v = (0, 3, 2, 1) u = (a) ||u|| (b) ||v|| (c) ||u + v||
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- Write v as a linear combination of u1, u2, and u3, if possible. v = (3, 0, −6), u1 = (1, −1, 2), u2 = (2, 4, −2), u3 = (1, 2, −4)Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (2, 1, 1), v = (3, 2, −1)express ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)=− 2/3 ,2.
- f(x) = x + 1, g(x) = 2x + 1, h(x) = 3x + 1, then are the functions f, g, and h linearly independent ?express ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)= 1 2,−2.(a) Show that the vector functions are linearly independent on the real line. (b) Why does it follow from Theorem 2 that there is no continuous matrixP(t) such that x1 and x2 are both solutions of x' = P(t)x?