(b) Given $B=\left[\begin{array}{ccc}1 & -1 & 0 1 -1 & 2 & -1 10 & -1 & 1\end{array} ight]$ (i) Find all eigenvalues of $B$, as well as the corresponding eigenvectors. [6 marks] (ii) Give a matrix $P$ that orthogonally diagonalises $B$. You must show that the matrix you have found works. [4 marks] (c) (i) Insert the missing entries $a, b, c$ that create a stochastic matrix $M=\left[\begin{array}{ccc}0.7 & 0.2 & 0.1 0.2 & 0.5 & 0.3 a & b & clend{array} ight]$ (ii) Show that $\left[\begin{array}{1}1 \\1\1\end{array} ight]$ is a steady state vector for this matrix. [1 marks] (iii) Explain why a vector in $\mathbb{R}^{n} $ comprising all l's as its components is a steady state vector for any $n \times n$ symmetric stochastic matrix. [2 marks] CS.VS. 1584