Question

Consider the matrix $\mathbf{A=\begin{bmatrix} -9 &4 \\ -24&11 \end{bmatrix}}$

b) Identify all subspaces of $\Re ^{2}$ that are invariant under $\mathbf{A}$.

Answer 1

A = 19.47 du CA-AT) = 0 7 -320 Note that (9 477.3117 -24 11 =) de 3-1 Invariant subspace o Aau so - zewodim subspate O espany (2), spank (1) One dan subspac spans/!),14? =rR? tuo dimensional subspace

(A - 37 = (-12 4 7 =o. - 124 = 40 - 32= This eigenveens of zis (13) and (A+ In = 0 5-8 487) = 0 1-24 12 lm] » 824 = 42 = 224 = 2 This eigenvector of - lis (2)

A = 19.47 du CA-AT) = 0 7 -320 Note that (9 477.3117 -24 11 =) de 3-1 Invariant subspace o Aau so - zewodim subspate O espany (2), spank (1) One dan subspac spans/!),14? =rR? tuo dimensional subspace