Let T: R2 ⟶ R3 such that T(a1, a2) = (a1-a2 , a1 , 2a1 + a2) Let β = {(0,1),(1,0)}       γ = {(2,2,3),(0,1,1),(1,1,0)} Find [T]βγ  If α = {(2,3),(1,2)} Find [T]αγ .

Q: Let x₁ = a +bt² +c+z₁, t=0, 1, 3,... where a,b and c constants and z, ~WN (0,0²). a) Let U₁ = x,…

A: Given, xt=a+bt2+c+zt , t=0, 1, 3, . . . where a, b and c constants and zt~WN0, σz2.

Q: Evaluate |(a,b)=(0,0) given that f(x, y) = 3x² + [y]; x = e²a+b₁ e²a+b; y = a² + t² + 1 да

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Q: Given the function g of the two real variables t and u by g(t,u)=t^2 + tu-u^2+(6+2)u c) Determine…

A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(6) = −4, g'(6) = −8,…

A: Step 1: Given that z=f(x,y),x=g(t),y=h(t) and…

Q: Choose the correct answer If f(x,y)=x2+2y2, then fx(2,1) and fy(2,1) are...  fx(2,1)=5, fy(2,1)=5…

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Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: Let f(x, y, z) = x2 (e)^y/z. Compute f(-1, 0, 1), f(1, 3, 3), andf(5, -2, 2).

A: Let fx,y,z=x2eyz 1. we have to compute f(-1,0,1) as, fx,y,z=x2eyzHere x=-1, y=0,z=1f-1,0,1=-12e01=1…

Q: Let f(x) = 2x + x² on [0,7]. Let o = {0,3,4, 7}. Let a(x) = 2x² on [0,7]. Give the numerical value…

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Q: Which of the following pairs of functions is linearly dependent?

A: Explained below

Q: x = x(u, v), y = y(u, v), with x(-1,6) = 1 and y(-1,6) = 5, calculate z,(-1,6) in terms of some of…

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