Let L: C[0, 1] → C[0, 1] be a linear map. If L(1) =x, L(x) =x^2, then what is L(3x + 2)?

Q: Determine all the 1-linear functions δ: M1×1(F)→F.

A: Given mapping is,

Q: Show that x – P VB + (d - x)* g(x) is a decreasing function of x.

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Q: Are the following functions are linear transformations? Explain why or why not. a) L : M2×2(R) → R,…

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Q: (3) Consider the linear map T : R? → R? which sends (1,0) (-3,5) and (0, 1) → (4, – 1). (f) Deduce…

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Q: Consider the the linear maps ƒ : R² → R² and g : R² → R² given by f((x, y)) = (x − y, 2 + y) and…

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Q: Let f: R² → R be defined by f((x, y)) = 7x - 5y. Is f a linear transformation? a. f((x₁, y₁) + (x2,…

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Q: 3. a) Use REGRESSION to find a quartic function y = ax* + bx3 + cx² + dx + e that fits the data. b)…

A: given y=ax4+bx3+cx2+dx+eUsing the regression to find the quadratic function

Q: Let : R³ → R¹ be a linear map such that /(1,2)=(1,1,2), and /(2, 1) = (2,2,1). Then which equalitie…

A: Let V(F) and W(F) be two vector spaces over field F and f:V→W be a linear map. Then, a)…

Q: Describe each of the following graphs in the xy-plane. Givejustification.(a) x = 0 (b) y = 0(c) x +…

A: a) The objective is to describe x=0 in the xy-plane. The graph of x=0 in the xy-plane is a vertical…

Q: 4. Consider the the linear maps f: R² R² and g: R² R² given by f((x, y)) = (x-y,2+ y) and g((x, y))=…

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Q: Suppose a smooth function f(x) satisfies f(0) = 0, f(1) = 2, and that f[x0,x1,x2] = 1  for any three…

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Q: Suppose a transformation has a mapping as follows:(x,y)→(1/2 x + 3, -2y + 4). If this mapping were…

A: Given: A function y=x and a transformation mapping x, y→12x+3, -2y+4.

Q: In(2 - a) x² + y² – 16' Determine the domain of the function f(x, y)

A: The domain of a function is the values of the variables of the function that result in a defined…

Q: 2. Is there a linear map from R³ to R³ such that T(1,3,0) (0,0,0) and T(-2,0,0) = (0,0,0) and T(3,…

A: We  have  to  find a  linear  transformation T: ℝ3 →ℝ3   for  which…

Q: If f(x) = x2 – 5x + 7, what are the co – ordinates of the minimum of y = f(x – 2)?

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Q: Let ƒ : R² → R be defined by ƒ((x, y)) = 2x + 5y + 3. Is ƒ a linear transformation? a. f((x1, y₁) +…

A: A transformation T:V→V is said to be a linear transformation if the following properties hold: 1. If…

Q: Let f: R² → R be defined by f((x, y)) = 6x- -9y - 9. Is f a linear transformation? a. f((x1, y₁) +…

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Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00⁰).…

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Q: Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

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Q: The map f:R³→→→→→→R³ defined by f(x,y,z) = (x+y+z,0,2) is a linear map. True False

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞, ∞). f₁(x)…

A: The given functions are

Q: Find all global minimum points of ƒ in R³, if ƒ (x1, x2, x3) = ex² + x½ + 2x²x3 + x² − 8x2 - 8x3

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Q: Find and classify

A: Given, the map                    xn+1=rxn(1+xn2), when r>0

Q: Define T : P4(R) → P4(R) by T(p)= ((3x^2 −4x+9)p)'' (a)  Show that T is a surjective linear map.…

A: It is given that T:P4(ℝ)→P4(ℝ) defined as T(p)=((3x2-4x+9)p)'' for p∈P4(ℝ)Basis for P4(ℝ) is {1, x,…

Q: True or False: The linear map T:P 3(R)->R^4 defined by Tp= (p(1).p(2).p(3).p(4)) is invertible. O…

A: Given: T: P3R→R4 defined by  Tpx=p1, p2, p3, p4T1=1,1,1,1Tx=1,2,3,4Tx2=1, 4, 9, 16Tx3=1, 8, 27, 64

Q: Find the value of b so that the point x = (13, b) belongs to the boundary of the set U = {x=R² : x₁…

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Q: 7. Find the minimum of, f(x1, x2) = 2x? – X1X2 + 2x³ + x³ – 2x1x3 And check the second order…

A: This is a problem of multi-variable calculus.

Q: Let f : R² → R be defined by f((x, y)) = 8x+2y + 2. Is ƒ a linear transformation? a. f((x₁, y₁) +…

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Q: Use the nodes ro = a - ya and r1 = a + ya to linearly interpolate a function f(r) on the interval [a…

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