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Problem 173

# Find the rank of matrix A where $$\mathrm{A}=\begin{array}{cccc} 1 & 0 & 2 & 3 \mid \\ 0 & 0 & 5 & 1 \\ 0 & 0 & 0 & 0 \end{array}$$

Expert verified
The given matrix A is already in Row Echelon Form: $$\mathrm{A}=\begin{array}{cccc} 1 & 0 & 2 & 3 \\\ 0 & 0 & 5 & 1 \\\ 0 & 0 & 0 & 0 \end{array}$$ The number of non-zero rows is 2, so the rank of matrix A is 2. Therefore, $$\text{rank}(A) = 2$$.
See the step by step solution

## Step 1: Identify the linearly independent rows

Since the given matrix A is already in Row Echelon Form, we can simply count the number of non-zero rows to find the rank. The matrix A looks like this: $$\mathrm{A}=\begin{array}{cccc} 1 & 0 & 2 & 3 \\\ 0 & 0 & 5 & 1 \\\ 0 & 0 & 0 & 0 \end{array}$$ We can see that there are two non-zero rows in the matrix.

## Step 2: Determine the rank of the matrix

Since there are two linearly independent rows, the rank of matrix A is 2. Therefore, rank(A) = 2.

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