If w Au +3v, then the u-elasticity of w is... 2v nw/u nw/u nw/u nw/u 3v 4u + 3v 4uv 4u + 3v 4u 4u + 3v 3uv (4u + 3v)²

Q: Example: Calculate the value of (@w/0x) at the point (x, y, z) = (2, -1,1) if:- w = x2 + y2 + z? z3…

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Q: 1 2 0 0 2 0 0 2 0 0 plain why span M2(R) 0 4 3 4

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Q: (3, 4, 3) Let v = Calculate: vxi=( vxj=( v x k = ( A F ->

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Q: u = [8, –1, –2] v = [0,7, 2] V u x v = [ Ex: 5

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Q: are linearly independent if and only if k # -0-2-0 v= -6 -1 + k 3 = 5 1 1 7

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Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: An object is acted upon by the forces F, = (12,6,4) and F2 = (0,5,8). Find the force F, that must…

A: Given that an object is acted upon by the forces F1and F2. We have to find the force F3 that must…

Q: 1 2 B =

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Q: d) S t3 – 2t2 – 1 dt t2

A: (d) We need to evaluate the following integral ∫13t3-2t2-1t2dt

Q: Is A = diagonalizable. Justify your conclusion. 10 120 -3 5 2,

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Q: Express the following as a linear combination of u= (3, 1, 7), v = (1, -1, 7) and w = (6, 3, 6).…

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Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: 8. Find the value of a if F = (axy-z)i+(x+2 yz) j+(y - axz)k is irrotational. %3D

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Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

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Q: A tank initially has 100 gallons of brine containing 5 lbs of salt. The mixture is kept well-mixed.…

A: A tank has initially 100 gallon of brine containing 5 lbs of salt and the mixture is kept…

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

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Q: a. Is S = {v1, V2, V3} linearly independent

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Q: Let u= 31-2j + k and v= 2i – 2j + 2k. Find ux y.

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Q: Find the stable vector of P || -

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Q: Determine

A: We use definition of linearly independent set.

Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

Q: 21 -2 and y -3 3 Express the vector v as a linear combination of a -4 y.

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Q: Let V₁ 3 and V3 5 Let S = {V₁, V2, V3). Determine ether S is linearly dependent, and (b) whether S…

A: We determine whether the set S is Linearly dependent and spans R3.