Suppose the solution set of a certain system of linear equations can be described as x₁ = 7+3x3, x2 = -4-5x3, with X3 free. Use vectors to describe this set as a line in R³. Geometrically, the solution set is a line through parallel to

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Q: show that T is a linear transformation by finding a matrix that implements the mapping. Note that…

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Q: 2. For universe S = R² define relation as: (a, b) ≤ (c,d) ⇒ 2a-b≤2c-d. For each of the properties…

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A: we have to show that  ≤ ≤ for any z and w in .

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Q: (5) Prove: 1 a) lim z+di Z→ 1-2i b) lim. 2-0 c) lim 730 1 (1M²)². 12₁²2² does not exist (Rez) -1-2-1…

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Q: The position vector of a particle moving along a helix is = = 4TT. c(t) = (cos(t), sin(t), t²). (a)…

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Q: 0 T/2 (sin² t cost + √1+ cos(2t)) dt

A: sin2t = 2Sint cost1 + cos2t = 2cos2t1 - cos2t = 2sin2t2cosA cosB = cos((A+B)/2) + cos((A-B)/2

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Q: Let T be the linear transformation defined by T(x1, x2, x3, x4) = 10x19x2-3x4. Find its associated…

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Q: Problem 3. K and torsion 7. In class, we showed that dī dB ds ds In this problem, we will justify…

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Q: 1. Consider the set of upper triangular 2 x 2 matrices, with real entries: b B = {(" "); GAVER} a,…

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Q: hree solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x-², and 3 = 3x-² + 8x.…

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Q: Find the simple interest Jolie owes on a 2-year loan for $8,000 to buy a used car at the rate of 9%…

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Q: 1. Write down the ODEs defining the streamlines of the time-independent (steady- state) flow u(x, t)…

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Q: EVALUATE e) ff dA y = x² +1, y = 3− x²

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Q: STATEMENTS 1.3.3 ED & 3D 1. ABD is a night angle ZEDB is right angle 90 3, 130 MEEDB-90 & ZABC+ZCBD…

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Q: a <b, A and B be constants. dx = S[y] = ["da (y² +w²y² + 2yz²4), v(a) = A‚_y(b) — B, a where w is a…

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Q: In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple…

A: Given:f(x, y, z)=cos(xyz),The Box B is given as B={(x, y, z)| 0≤x≤11, 0≤y≤11, 0≤z≤11}.

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Q: Let the universal set be R, the set of all real numbers, and let A = {x ER | -3 ≤ x ≤ 0), B = {xER…

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Q: Consider the following planes. 5x + 2y + z = -1 and 2x -y + 6z = 9 Use these equations for form a…

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Q: For the case a = 0, b = 1, find a stationary path of S[y] for the boundary conditions y(0) =…

A: (.)   The stationary path of  is,                         we find stationary path  for the boundary…

Q: Determine the indicated values for the function f(x,y)=2x²y. O8y8 O2y1 O1y4 O 10 y 8 fx(2.1); f,…

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Q: 2. Consider the function z = f(x, y) = 2x+y-2. a) What shape is the graph of z=f(x,y)? Does the…

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Q: (e" + 1)² e "dx + (e + 1)³ edy=0

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Q: Evaluate the following limits: a) lim x1x2+9 2 b) lim 4x x-01+e-x c) lim x-0 √x+1-1 x

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Q: The revenue (in dollars) from the sale of a infant car seats is given by R(x) = 67x -0.02x², 0≤x≤…

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Q: 5. New York Building Corporation uses the critical path method to monitor construction jobs. The…

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Q: .Write the equation of the graph below (-3,9) (-2,5) 10 9 8 7 6 5 + (-1.3) (0, 2) 1 --5-4-3-2-1, +…

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