Let A e Mnxn(F) be upper triangular. Prove that det(A) is the product of the diagonal entries.

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Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

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A: (Solving the only one question as per our guidelines) Question: Let x∈ℂm and y∈ℂm Show that x,y=y*Ax…

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A: Given, U2=I

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Q: The linearization at a = 0 to V6+ 5x is A+ Bx. Compute A and B %3D A = %3D B = %3D

A: Consider the given: Let fx=6+5x    at x=af0=6+50f0=6+0f0=6

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A: Given that, A is invertible and DA=CA.

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Q: Prove that if A ∈ M 2×2(F) is upper triangular, then det(A) equals the product of the diagonal…

A: Let the matrix A be the upper triangular matrix as follows.

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Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

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A: Firstly, find out Tz*.

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Q: fx) =x+x, aニー %3D LCx) = ? %3D

A: Our objective is to find the linearization L(x) at x=a.

Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension.

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Q: Let R=[0,6]×[0,6]. Subdivide each side of R into m=n=3 subintervals, and use the Midpoint Rule to…

A: Given :  R=0,6×0,6m=n=3     MIDPOINT RULE:

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Q: Let T: 1 1 be defined by (1, 62, E3,) (0, 0, 6, E). Is T bounded? Self-adjoint? Positive? Find a…

A: As this is a multiple sub-part question, according to the Bartleby Answering Rule, only first three…