2. Use Wronskian to show that fi = x, f2 - Inz, and fa C (R). z Inz are linearly independent in

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Q: Use the change of variables X1 X2 X3 X4 = = G(r, 01, 02, 03): = to compute the content of the 4-ball…

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Q: fi(x) 1 A = {fi, f2, f3} c F(R) and f(x) = f:(x) = |x+ 1| PROVE: A is linearly independent. (A L.I.)

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Q: -2y 2x (x²+y²) ²³ (x²+y²)² Compute fF.dr, where F(x, y) = oriented counterclockwise. (Use symbolic…

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Q: e equation of

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Q: Q.4.(a). Show that the following functions is not an inner product on R3, where u = (u, U2, U3) and…

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Q: Prove that I(r + 1) = ar(r). 3. ii. Prove th at 3(m, n) = B(m + 1, n) + B(m, n+ 1). %3D

A: The required proofs are detailed below.

Q: 2. Let g (x, y) = 2x² – y² . Compute 9(1, 2), g (2, 1), g (1, 1), g (–1, 1) and g (2, –1).

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Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: 6. The function f(x, y) = (x², y², xy) is a function of f : C² → C³. Determine whether the function…

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Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

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Q: 1. Let f(x, y) = x + 2y. Find f (0, 1), f(2, -1), f(a, a), and f(a + h, b) - f(a, b).

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Q: 4. Let Z[V2]= {a+b /2]a,b e Z}. Define addition and multiplication on Z[ /2] as follows: (a+b [/2])…

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Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: Let f(x,y) = x - 5xy -y². Compute f(6,0), f(6, – 2), and f(b,c).

A: Solved below

Q: Ques. 3: Check whether the operator T: R2 → R2 defined by T(x, y) = (y,x) is linear. Moreover if T…

A: A mapping T:R2→R2 is a linear transformation if and only if a) T(u)+T(v) = T(u+v) b) T(cu) = cT(u)…

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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