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Question: bycalculatingthecharacteristicpolynomialeigenvaluesanddimensionsoftheeigenspaces of each map or matrix below determine if the...

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Bycalculatingthecharacteristicpolynomial,eigenvaluesanddimensionsoftheeigenspaces of each map or matrix below, determine if the given map or matrix is diagonalizable. If a map or matrix is diagonalizable, diagonalize it (linear algebra)

1. By calculating the characteristic polynomial, eigenvalues and dimensions of the eigenspaces of each map or matrix below, determine if the given map or matrix is diagonalizable. If a map or matrix is diagonalizable, diagonalize it (that is, give a basis consisting of its eigenvectors) The field F over which you consider the problem is given in each part (a) A-01 0over an arbitrary field F 0 0 2 (b) A-0 0over an arbitrary field F 0 0 2 (c) T: P2(RP2(R) given by T(ax2 +bx +c) cx2ax + b (Here F R.) (d) T: P2(C)P2(C) given by T(ax2+bxc)cxax+b (Here F C.)

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