A linear operator T and bases B1 and B2 are given. a. Find [T]B1 and [T] B2 b. Verify that the action on v of the linear operator T is the same when using the matrix representation of T relative of the bases B1 and B2

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Q: For matrix A and a scalar k, (kA)T is equal to: k(A^T) k(A) (k^2) x (A) (k^2) x (A^T)

A: We will solve the matrix operation.

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A: According to Cayley Hamilton theorem, any square matrix satisfies its own characteristics.

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A: Ansa; Consider, 10=a11+b3-1⇒10=a+3ba-b⇒a-b=0⇒a+3b=0slove both equation and get;a=b=14 Co-ordinates…

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A: To determine whether the matrix operator in each part is invertible. a) T(x, y)= (x+3y, 2x+5y)

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A: Solution is below.

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A: A=2-349 Characteristic equation of A is given by  λ2-trAλ+detA=0 , where trA, detA denote the trace…

Q: Let B1 = {T1,t2, t 3} and C, = {w1, w2, w3} be two bases for R³ such that । = - , के = - े;, के; =…

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Q: Let T : R? → R´be defined by [2 _5||X1 X2 1 6] [x2] а If B = is a basis for R“ such that |T'|B is a…

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Q: Prove that for any matrix A ∈ Mm×n(F), (R(LA∗))⊥= N(LA).

A: The objective is to prove that

Q: Let T : R² -> R² be defined by T ( 3x1 – 12 -1 B = 2 , and | . Let u = %3D -3x1 + x2. {{}} C = Given…

A: Consider the given information.

Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: P1→P1:…

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Q: Let L be the linear operator on R³ defined by 2x1 – x2 – X3 L(x) = | 2x2 – x1 – X3 2x3 – X1 – X2…

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Q: Let C be a fixed n × n matrix. Determine whetherthe following are linear operators on Rn×n: L (A) =…

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

A: T(x, y) = T2 o T1 (x, y)              = T2 (x - 4y, 3x + 2y)              = (0, x - 4y)…

Q: Find a basis for the kernel of the linear operator T(x, y) = (6x - y, -24x + 4y), Using the…

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A: Now the transpose is,

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Q: 12. Let 1 2 3 4 M = and T be the linear operator on V defined by T(A) = M A. Find the matrix…

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Q: Consider the matrix 0 an 0 0 where aan aye 0. Show that A is invertible and find its inverse.…

A: You have posted multiple questions. We are solving only the first one. If you need an answer to…

Q: Determine whether the given linear operator/matrix is diagonalizable. (a) T: R³ → R³ with T(1, 1, 1)…

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Q: 2. Determine whether the matrix operator T: R2R2 defined by the equations is invertible; if so, find…

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Q: Let B= {b1, b2} and c= {cl, c2} be bases for a vector space V, and suppose b1 = - cl + 4c2 and b2 =…

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Q: Let Mı5(IR) = {A/A and 15th order square matrix with real elements} and consider the linear…

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Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: P2→P2:…

A: Given, the map               We have to find the basis B for the domain of T s.t. T relative to B…

Q: x + y x +y 3. Т y B1 = {e1, e2} %3D {[:}(=} - B2 = 1 3 V = -2

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Q: y 13. T y | B1 %3D B2: %3D 1

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Q: (a) Find the matrix representation of L(x), the linear operator on R? that first rotates by 30°…

A: Vectors.

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Q: Let T be a linear operator defined on P3 by T(a0+a1x+a2x^2)=a0+a1(x-1)+a2(x-1)^2. The third row of…

A: Option (a) is correct

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Q: Assume the mapping T: P2 → P2 defined by T(ao +a,t+a,t) = 6a0 + (3ao - 5a,)t+ (7a, +2a2)ť is linear.…

A: Consider the linear mapping T : ℙ2→ℙ2 defined by Ta0+a1t+a2t2=6a0+3a0-5a1t+7a1+2a2t2  We have to…

Q: (E) E} ED- -3x1 Let T : R³ → R² be defined byT 3x2 + x3 X3 -6° Let B = -5 ,u2 = -3 , U3 = and C = Vị…

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Q: Determine whether the matrix operator is invertible, if so, find its inverse. a)T (x, y) (x+ 2y,-x+…

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Q: Determine whether the given linear operator/matrix is diagonalizable. (@) c = [ 2² ] C (b) T: R³ R³…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…