42. Let M be 2x2 matrix with real entries. Consider the linear system of ODE given in the vector rotation dx(t) dt =Mx(t) and x(t) = [u(t), v(t)]T. then pick out the case when lim u(t)=0, lim v(t) = 0: 1-00 (A) M= -[ (B) M= (35w- (C) M= -5 11 0-7] 17] [27] 03 M = [-5₁ (D) M= M = [₁ 0 9] -51 3 -5 5 -7

Q: C: Let T be the linear operator associated in the standard basis B of F2 with the matrix 2 - [34] -2…

A: C. Given that be a linear map whose associated matrix with respect to standard basis  is    .In…

Q: a) Let T: R² R² be a linear transformation given by T(x, y)-(x+y,x-y). Find the matrix for T…

A: For (a), We are given that T: ℝ2→ℝ2 be a linear transformation given by T(x, y)=(x+y, x-y).  Now, we…

Q: Consider f(t) = (cos t, sin t, t?) and g(x, y, z) = (x² + y² + z², 3x + 4y – 12z) and h = g(f(t)) =…

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Q: Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let 23 A- [²8] 40 be the…

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Q: Find the matrix A' for T relative to the basis B'. Tea T: R² → R², T(x, y) = (x − y, y − 3x), B' =…

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Q: 1. Let A=MB (f) be the matrix associated with the linear map f(x,y,z) = (2x-2y+z, x-4y+z, x-y-z)…

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Q: {H} Let B = and B' Find the change of base matrix from B' to B and from B to B'

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Q: Let c1 (t) = ei + 7 sin(t)j + t*k and c2 (t) = e-Sti + 5 cos(t)j – 7t*k. (Enter your solution as a…

A: Given: Let c1(t)=e5ti+7sintj+t4k and c2(t)=e-5ti+5cos(t)j-7t4k. To Find:      ddt[c1(t)+c2(t)]

Q: 3. Consider the two bases for R given by B = {(1, 1), (-1, 1)} and B' = {(-1, –1), (–1, 1)}. Find…

A: From change of basis concept.

Q: 4. Given two bases (b) = transformation y : R² → R² with respect to the basis (f) and let X, be a…

A: Given two bases b=b1,b2 and f=f1,f2 of ℝ2  where  b1=12, b2=34, f1=11, f2=23 Let Af be a matrix of a…

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A: The given transformation is Tx,y=x-y,y-4x and the basis B'1,-2,0,3.

Q: assume thatf (2, 3) = 8, fx (2, 3) = 5, fy (2, 3) = 7 Which of (a)–(b) is the linearization of f at…

A: Consider the given: f2,3=8fx2,3=5,fy2,3=7,

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Q: Determine the real root of -12- 21x + 18x² - 2.75x³ graphically (choose your limits). In addition,…

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Q: Find the matrix A' for 7 relative to the basis 8'. A' = T: R² R², T(x, y) = (x − y, 4y − x), B′ =…

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Q: Let e(x) = 1- 4t + 3t² € E₂. Consider the following ordered bases for E B = {1, t, t²} and B' = {t²,…

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Q: Find the standard matrices A and A' for T = T₂ ° T₁ and T' = T1 ° T₂. T₁: R² R², T₁(x, y) = (x - 5y,…

A: T1: R2 → R2, T1(x, y) = (x − 5y, 5x + 4y) T2: R2 → R2, T2(x, y) = (y, 0) Now T = T2 o T1 (x,y) = T2…

Q: Find the standard matrices A and A' for T = T₂ ° T₁ and T' = T₁ ° T₂. T₁: R² - R², T₁(x, y) = (x -…

A: Given T1:ℝ2→ℝ2 by T1(x, y)=(x-2y, 2x+3y), T2:ℝ2→ℝ2, T2(x, y)=(0, x)   To Find: The standard matrices…

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A: Note: Since you have posted a question with multiple sub-parts, we will solve the first three…

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Q: 4' for T- T2• T, and T- T1• T2. x - 5y, 4x + 2y) y, 0)

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Q: ind the matrix A' for T relative to the basis B'. T: R² → R², T(x, y) = (-2x + y, 2x - y), B' = {(1,…

A: Given : T : R2→R2, T(x,y)=(-2x+y,2x-y),B'=1,-1,-1,5 . To find : The matrix A' for T relative to the…

Q: TV T(x, y,2)=(xry, q-2, x-2) 1. Fond the matrix A represmting T Fnd matrix B repregenty 2. 3.…

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Q: Example 3: Find the coordinate matrix of x (3, 19, 2) in R³ relative to the basis B' = {(8, 11,0),…

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Q: 0 1 1 (₁2) (₁) (1₂) Calculate matrix = = (A – AT)² and vector w = Bx. Then, Consider matrix A = X =…

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Q: Let B = {(1, 3), (-2,-2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let - [28] 24 be the…

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Q: Let T: R² → R³ and S: R³ → R² be two linear transformations. Suppose the matrix of T is 21 -1 and…

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Q: 1. Let A=MB.(f) be the matrix associated with the linear map f(x,y.z) = (3x-y + 4z.y+z-x.x+y+z)…

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Q: {(1, 1), (-2, 3)}, B' = {(1, –1), (0, 1)} be bases for R?. [3 2] Let B Let A = be the matrix for T:…

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Q: Consider the functions f(x, y, z) = xyz and g(t) = (cos(27t), sin(27t), e*) 6. (a) Compute Df(1,0,…

A: f(x,y,z)=xyz(a) Df=i^∂f∂x+j^∂f∂y+k^∂f∂z   =i^∂∂x(xyz)+j^∂∂y(xyz)+k^∂∂z(xyz)…

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A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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Q: linear transformation A maps P(1,0) to P’(-2,-4) and Q(0,1) to Q’(4,1). Find (i) The matrix A (ii)…

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Q: U₁ = -0₁ --- --- -- = = V2 = (a) Find the transition matrix from the basis E = {v1, v2} to the basis…

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Q: (а) T(г, у) — (т, -у); (b) T(г, у) — (2г, 5у): (с) T(т, у) — (т+у, y):

A: We have to find the canonical form of the linear transformation. We choose the canonical basic for…

Q: Let A=Mb (f) be the matrix associated with B the linear map_ƒ((x,y,z)=(x − 2y,y+z,0) relative to…

A: