A ={{4,-1,-7,0},{8,-5,-7,0},{-6,-1,3,0},{-6,-1,7,-4}}

MatrixForm [A]

c = CharacteristicPolynomial [A,t]

Factor[c]

Aplus4E = A + 4 * IdentityMatrix[4]

B = Aplus4E

U = NullSpace [Aplus4E.Aplus4E.Aplus4E]

NB3 = NullSpace [B.B.B]

NB2 = NullSpace [B.B]

NB1 = NullSpace [B]

x21 = {1,0,1,0}

B.x21

x11 = NB1[[1]]

BU = {B.x21, x21, x11}

BV = NullSpace [A - 10* IdentityMatrix [4]]

BB = Join[BU, BV]

J = Inverse [Transpose [BB]]. A. Transpose [BB]

MatrixForm [J]