Suppose T: R² → R4 is a linear transformation with T(₁) - (standard) matrix A such that T(x) = Ax. NOTE: e; refers to the ith column of the n x n identity matriu 13 4 12 12 T(e₂) = 9 14 -16 10 . Find the

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A: Augmented matrix of the given system is  -4101-1201-410-13001-41-40101-4-30

Q: Let A = -5 6 -2 3 -11 14 and define T: R² → R² by T(7) = Az. Find T 5. Find 7 ([^;])-4-[-'₁). = A.

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Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

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Q: Let A be the following matrix: A = Find the scalar multiple –5A: 0 -3 2 3

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A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: Set up the matrix which will perform the following transformation and write down its character. (x…

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Q: Find the QR factorization of the matrix   Please show all work

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Q: Consider the following function; Q(x1, x2, X3) = 2x? + 3x? – xž + 5x1x3 + x2x3 Find the matrix A…

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Q: Find the matrix of the reflection about the line L.

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Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

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Q: -37 -1 0 -1 4 0 -1 -1 4 -1 0 A = 3

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A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Let A be a 2 x 2 matrix a If ad – bc + 0, then A-1 ad-be ad-be ad-e ad-be. such that [1 AA-1 = A-'A…

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Q: Suppose A has row echelon form - 8 - 36 - 36 0 0 0 - 0 0 6 8 – 40 0 - 9 5 6 - 12 The following row…

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Q: 0 0 1 -1 0 0 -1 2002

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Q: in

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Q: Define T: R² R³ by T ([2]) 211 - 212 - 12 21 +372 Then we can write T(z) – Az where A =

A: If T is a linear transformation from Rn to Rm such that T(x) = Ax then A is an mxn matrix.