https://file.aiquickdraw.com/mathbot/file/1729205382570jxlsk0h5.jpg

To determine the second row of the matrix \( A \), let's first note what it means for a matrix to be stochastic:

1. **Definition of a Stochastic Matrix:** Each row of a stochastic matrix must sum to 1, and all entries must be non-negative.

The given matrix is:
\[
A = \begin{bmatrix} 0.6 & 0.5 \\ ? & ? \end{bmatrix}
\]

For \( A \) to be a stochastic matrix:
- The sum of the elements in each row must equal 1.

### Step 1: Find the second row.
Let the second row be \( [a, b] \). Then:
\[
a + b = 1
\]

The image indicates that the second row is given as \( [0.4, 0.6] \), so:
\[
0.4 + 0.6 = 1
\]
which satisfies the requirement for a stochastic matrix.

### Step 2: Verify the steady state vector.
The steady state vector for \( A \) is given as:
\[
\begin{bmatrix} \frac{5}{9} \\ \frac{4}{9} \end{bmatrix}
\]
This vector satisfies \( A \cdot v = v \), indicating that it is indeed the steady state.

If you would like further details on why this vector is the steady state or have other questions, let me know.

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Here are five questions related to the topic:
1. How do you compute the steady state vector of a stochastic matrix?
2. What properties must a matrix have to be considered a Markov matrix?
3. How would the steady state vector change if the matrix was modified?
4. What are the applications of steady state vectors in real-world problems?
5. How can one determine the convergence rate of \( A^n \cdot v \) as \( n \to \infty \)?

**Tip:** To find the steady state vector for a stochastic matrix, solve the equation \( A \cdot v = v \), where \( v \) is a probability vector (its components sum to 1).

What is the second row of the matrix A if A is stochastic?

Learn how to find the second row of a stochastic matrix and compute the steady state vector. This problem explores key concepts in matrix algebra, such as stochastic matrices and steady state vectors, with a solution for a matrix A where the second row sums to 1.

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