### 15. Consider again the system [ mathbf{x}^{prime}=mathbf{A} mathbf{x}=left(begin{array}{rr} 1 & -1 \ 1 & 3 end{array}right) mathbf{x} ] that we discussed in Example 2. We found there that ( mathbf{A} ) has a double eigenvalue ( r_{1}=r_{2}=2 ) with a single independent eigenvector ( xi^{(1)}=(1,-1)^{T} ), or any nonzero multiple thereof.

15. Consider again the system [ mathbf{x}^{prime}=mathbf{A} mathbf{x}=left(begin{array}{rr} 1 & -1 \ 1 & 3 end{array}right) mathbf{x} ] that we discussed in Example 2. We found there that ( mathbf{A} ) has a double eigenvalue ( r_{1}=r_{2}=2 ) with a single independent eigenvector ( xi^{(1)}=(1,-1)^{T} ), or any nonzero multiple thereof.