Question

(1.) If \( T={ }_{B}^{A}\left(\begin{array}{cc}0.25 & 0.75 \\ 0.3 & \alpha\end{array}\right) \) is a transition probability matrix, then the value of \( \alpha \) is a) \( 0.5 \) b) \( 0.7 \) c) 0 /d) \( 0.6 \) 2. Rank of matrix \( \left(\begin{array}{cccc}1 & -1 & 2 & 0 \\ 0 & 2 & 0 & 3\end{array}\right) \) is a) 1 b) 0 c) 2 d) \( -1 \)

Comments

Is there any answer

Answer 1

(1) ∵ Row sum of a transition probability matrix must be 1.

∴ 0.3 + α = 1

(sum of probability of 2^nd row)

\(\Rightarrow\) α = 1 - 0.3 = 0.7

(2) \( \begin{bmatrix} 1 & -1 & 2&0 \\[0.3em] 0 & 2 & 0&3 \\[0.3em] \end{bmatrix}\)

∴ Rank of matrix is 2.