Question: Determine explicitly the expression of the linear operator T over R 4 , diagonalizable, which simultaneously meets the following conditions: Ker (T) = {(x, y,

Determine explicitly the expression of the linear operator T over R4, diagonalizable, which

simultaneously meets the following conditions:

Ker (T) = {(x, y, z, t) R4 / x y z + t = 0 e z t = 0}

Im(T) = [(1, 0, 0, 0),(0, 1, 1, 0)]

= 2 is an eigenvalue of T with algebraic multiplicity equal to 2.

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