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33. T(x1,x2,X3) = (3x1, x2, X1 – x2)

33. T(x1,x2,X3) = (3x1, x2, X1 – x2)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 16E
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In Exercises 30-33, find the standard matrix A for the given linear operator, and determine whether that matrix is diagonalizable. If diagonalizable, find a matrix P that diagonalizes A. 30. T(x1,x2) = (2x, – x2,X1 + x2) 31. T(x1,x,) = (-x2, -x1) 32. T(x1,x2,X3) = (8x1 + 3x2 – 4x 3, – 3x1 + X2 + 3x3, 4x, + 3x,) 33. T(x1,x2,x3) = (3x1,x2, X1 – x2)
Transcribed Image Text:In Exercises 30-33, find the standard matrix A for the given linear operator, and determine whether that matrix is diagonalizable. If diagonalizable, find a matrix P that diagonalizes A. 30. T(x1,x2) = (2x, – x2,X1 + x2) 31. T(x1,x,) = (-x2, -x1) 32. T(x1,x2,X3) = (8x1 + 3x2 – 4x 3, – 3x1 + X2 + 3x3, 4x, + 3x,) 33. T(x1,x2,x3) = (3x1,x2, X1 – x2)
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