Step 2: Identify the rows of the matrix: Row 1 = [2, 3, 1], Row 2 = [1, 0, 2], Row 3 = [0, 1, 3].
Step 3: Check if the rows are linearly dependent. This means we need to see if one row can be made by combining the others.
Step 4: Notice that Row 3 can be formed by combining Row 1 and Row 2. Specifically, Row 3 = Row 1 - 2 * Row 2.
Step 5: Since the rows are linearly dependent, the determinant of the matrix is 0.
Determinant Calculation – The determinant of a matrix is a scalar value that can be computed from its elements and provides important properties about the matrix, such as whether it is invertible.
Linear Dependence – Rows (or columns) of a matrix are linearly dependent if at least one row (or column) can be expressed as a linear combination of others, which results in a determinant of zero.
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