grandes-ecoles 2017 QII.D.1

grandes-ecoles · France · centrale-maths1__official Matrices Projection and Orthogonality

We return to the example of subsection II.B with $\mu = 1$, i.e., $$A(1) = \left(\begin{array}{ccc} 1 & -1 & 1 \\ -1 & 1 & 0 \\ 0 & -1 & 1 \end{array}\right)$$ How should we choose $N^{\prime} = \left(\begin{array}{ll} N_{1}^{\prime} & N_{2}^{\prime} \end{array}\right)$ so that $\operatorname{det}\left(N^{\prime\top} A N^{\prime}\right) = 0$?

We return to the example of subsection II.B with $\mu = 1$, i.e.,
$$A(1) = \left(\begin{array}{ccc} 1 & -1 & 1 \\ -1 & 1 & 0 \\ 0 & -1 & 1 \end{array}\right)$$
How should we choose $N^{\prime} = \left(\begin{array}{ll} N_{1}^{\prime} & N_{2}^{\prime} \end{array}\right)$ so that $\operatorname{det}\left(N^{\prime\top} A N^{\prime}\right) = 0$?

Paper Questions

QI.A.1 QI.A.2 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.C.1 QI.C.2 QI.C.3 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.A.5 QII.A.6 QII.A.7 QII.A.8 QII.B.1 QII.B.2 QII.B.3 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QII.C.6 QII.C.7 QII.C.8 QII.D.1 QII.D.2 QII.E.1 QII.E.2 QII.E.3 QII.E.4 QII.E.5 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C.1 QIII.C.2 QIII.C.3