Let L:P1 --> P2 be a function defined by L(p)=tp + 1.
Where p is a linear polynomial in P1.
which of the following is not true?
L is a linear transformation |
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L is not a linear operator |
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L is not a linear transformation |
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L is not a 1-1 function |
Let L:P1 --> P2 be a function defined by L(p)=tp + 1. Where p is a...
Let L:P1 --> P2 be a function defined by L(p)=tp + 1. Where p is a linear polynomial in P1. L(t+1)+L(t-1)=? 2t^2 + 2 2t^2 + 3 t^2 + t + 2 3t^2 +t+1
8. Let L: P2 → P be the linear transformation defined by Lar? +bt + c) = (a + b)t +(b - c). (a) Find a basis for ker L. (b) Find a basis for range L.
Let V P2(R) and let T V-V be a linear transformation defined by T(p)-q, where (x)(r p (r Let B = {x, 1 + x2, 2x-1} be a basis of V. Compute [TIB,B, and deduce if it is eigenvectors basis of
Let f be the function defined below on the given region R, and let P be the partition P=P1×P2. Find Uf(P). f(x,y)=3x+4y R:0≤x≤2,0≤y≤1 P1=[0,1,3/2,2],P2=[0,1/2,1] a) Uf(P)=23/4 b) Uf(P)=37/4 c) Uf(P)=39/4 d) Uf(P)=93/8 e) Uf(P)=57/4 f) None of these.
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let T: P2 --> R be the linear transformation defined by T(p(x))=p(2) a) What is the rank of T? b)what is the nullity of T? c)find a basis for Ker(T)
Let T : P2 --> P4 be the transformation that maps a polynomial p(t) into the polynomial p(t) + t2p(t). (a) Find the image of p(t) = 2 - t + t2 (b) Show that T is a linear transformation. (c) Find the matrix for T relative to the bases {1, t, t2} and {1, t, t2, t3, t4}
P3. Define the hyperbolic distance between P and to be dH(P,Q) Ina, where a is defined in P2. Prove that da(P,) d(TP, TQ), where T - To,o is a horizontal translation. P3. Define the hyperbolic distance between P and to be dH(P,Q) Ina, where a is defined in P2. Prove that da(P,) d(TP, TQ), where T - To,o is a horizontal translation.
Problem #3: Let T: P2 P2 be the linear transformation defined by 7{p()) = (3x + 7) - that is 7(00+ cx + cox) = co + C (3x + 7) + C2(3x + 7)2 Find [7)with respect to the basis B = {1,x?). Enter the second row of the matrix 17 into the answer box below. i.e., if A = [718. then enter the values a1. 422, 223, (in that order), separated with commas. Problem #3:
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...