= Let p(x) = x³ x² + 2x + 3, q(x) = 3x³ + x² − x − 1, r(x) = x³ + 2x + 2, and s(x) = 7x³ + ax² +5. The set {p, q, r, s} is linearly dependent if a = -

Q: Let F = Q, s(x) = x² + 1, and E = Q[r]/(x² + 1)Q[x]. i) Factor the polynomial r? +1€ Q[r] into…

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Q: 6. Determine whether the following set of polynomials is linearly independent or not. (1 – t)?, t –…

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Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

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Q: 4. Let aj = 9. and b = 63 , a2 = 45 (a) Write b as a linear combination of a1 and a2. b = aj + a2.…

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Q: For which value of x is A = x = 4 1 -4 4 0 -3 0 1 x NOT invertible?

A: The objective of this question is to find the value of x for which the given matrix A is not…

Q: Let X and Y denote be as follows: E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) =…

A: Given data E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) = 155.  W = 2X-Y and  T =…

Q: Let fi (2) = - 5x – 5, f2(x) = – 6x² – 8x – 3, f3(x) = 2a² + 10x + 3, and fa(x) = 2x – 9. Find a…

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Q: Example 7. Show that T: E2 → E2, defined by is not linear T((x₁, x₂)) = (x₁ + x2, x1 - x₂ +1)

A: as we now for a linear map T(01 ) = 02  where 01 is zero of domain and 02 is zero of codomain

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: Let B = a = The function p(t) = 2 + 4(t − 5) + 7(t − 5)², can also be written as p(t) = a + b(t − 2)…

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Q: Consider the set S = {x² + 1, 2x − 2, − x² + x}. The set S spans P2. If t(x) = = 2x² 16x + 10 € P₂,…

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Q: If R and S are partial orders, then must ROS be a partial order? If not, explain why. Where is the…

A: Please see the below picture for detailed solution.

Q: Is T linear? If Yes find KerT, where T(x1, x2, x3) = (x1+x3, x1-x3, x2 )

A: Given Tx1,x2,x3=x1+x3,x1−x3,x2 We have to show that T is linear and then find the KerT Let…

Q: Consider the set S = {2x² + 1, 2x – 4, 2x + x}. The set S spans P2. If t(a) — 6а? + 6х — 15 € Ра,…

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Q: (c) Determine the values of a and b if T(x,y,z) = (2x+y+z,a+3y,b+4z) is not self- adjoint.

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Q: g is a coordinate system for a line L and a ∈ R, then the function f : L → R given by    f(P) =…

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Q: The domain of f(x) = V x2 + x – 6 | is : a) ]-4, 1[ b) ]-00, 4[U]1, +0[ c) ]-00,-3[U]2, +00이 d) ]-3,…

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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: Example 23: Show that, if Y (t) = X (t + a) – X (t – a), then, (i) Ryy (t) = 2 Rxx (t) – Rxx (T +…

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Q: If ů, = |8|,02 = 5,03 show that {v1, v2, v3} is linearly dependent in R', and determine the linear…

A: Letv1=2i^+8j^+3k^v2=i^+5j^+2k^v3=i^+j^Let…

Q: . Decide which of the following sets are linearly independent in R. Justify your answer in each…

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Q: Q4. Given three agents with states xi, i = (1,2,3). The agents are connected together and they…

A: Solution of part (a): It is given that xi.(t)=∑j=13xjt-xit. So,…

Q: Let T:P2(R) → P2(R) T(a + bx + cz?) = 3a – 16 + 6c + ( – 1la + 4b – 22c)z + (– 6a + 36 – 1lc)z? Let…

A: Let us us consider the mapping T:P2ℝ→P2ℝ be defined by Ta+bx+cx2=3a-b+6c+-11a+4b-22cx+-6a+3b-11cx2…

Q: All computations must be shown. 1. Let pi(t) = 1+ t², p2(t) = t +t² and p3(t) = 1 + 2t + t² be…

A: Consider the provided question, given,p1t=1+t2p2t=t+t2and p3t=1+2t+t2

Q: {r, u, d) is a set of linearly independent vectors. If x = 3r+ 5u + 2d, determine whether T = {r, u,…

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Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

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Q: Let us say that you are sitting at a coffee shop and you want to impress your significant other by…

A: As per bartleby guidelines for more than three subparts in a question only first three should be…

Q: real coefficients. Let p1(t) = 1–t+t², p2(t) = 2t – 3t², p3(t) = -1+t+2t² be elements of V. (a) Are…

A: Answer

Q: Find the general formula for T: R3 -> R3, if T(1,0,1) = (1,2,0) , T(1,-2,1) = (0,1,0) and T (0,0,1)…

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Q: Let →a=⟨7,−5⟩ and b→=⟨1,3⟩. Compute the dot product. →a X →b=

A: Given a→ = 7,-5 and b→ = 1, 3. We have to compute the dot product a→·b→.