grandes-ecoles 2013 QIII.E.4

grandes-ecoles · France · centrale-maths2__pc Invariant lines and eigenvalues and vectors Geometric interpretation of eigenstructure
Write a procedure or function in Maple or Mathematica that takes as input a quadruple $(a,b,c,d)$ of reals and returns a quadruple $(k, \ell, t, t')$ such that if $A = \left(\begin{array}{ll} a & b \\ c & d \end{array}\right)$ we have $f_A = k\rho_t + \ell\sigma_{t'}$. 
Write a procedure or function in Maple or Mathematica that takes as input a quadruple $(a,b,c,d)$ of reals and returns a quadruple $(k, \ell, t, t')$ such that if $A = \left(\begin{array}{ll} a & b \\ c & d \end{array}\right)$ we have $f_A = k\rho_t + \ell\sigma_{t'}$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QI.C.1 QI.C.2 QI.C.3 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C QIII.D.1 QIII.D.2 QIII.D.3 QIII.E.1 QIII.E.2 QIII.E.3 QIII.E.4 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.A.5 QIV.A.6 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QV.A.1 QV.A.2 QV.B.1 QV.B.2 QV.C.1 QV.C.2