Let T : P2 → P2 be the linear transformation such that T(1) = 4+ 2x + x², T(x) = 3x, T(x²) = 1+2x + 4x? 1. Is A diagonalizable? If so, find an invertible matrix P such that P-'AP = D 2. Find the eigenvalues and corresponding eigenspaces of T.

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Chapter7: Eigenvalues And Eigenvectors
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Let T : P2 → P, be the linear transformation such that
T(1) = 4+ 2. + x²,
T(x) = 3x, T(x²) = 1 + 2x + 4x?
1. Is A diagonalizable? If so, find an invertible matrix P such that
P-1АР — D
2. Find the eigenvalues and corresponding eigenspaces of T.
Transcribed Image Text:Let T : P2 → P, be the linear transformation such that T(1) = 4+ 2. + x², T(x) = 3x, T(x²) = 1 + 2x + 4x? 1. Is A diagonalizable? If so, find an invertible matrix P such that P-1АР — D 2. Find the eigenvalues and corresponding eigenspaces of T.
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