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(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 \( \alpha \) isa) \( 0.5 \)b) \( 0.7 \)c) 0/d) \( 0.6 \)2. Rank of matrix \( \left(\begin{array}{cccc}1 & -1 & 2 & 0 \\ 0 & 2 & 0 & 3\end{array}\right) \) isa) 1b) 0c) 2d) \( -1 \) |
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Answer» (1) ∵ Row sum of a transition probability matrix must be 1. ∴ 0.3 + α = 1 (sum of probability of 2nd 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. |
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