Step 1: Write down the matrix you want to evaluate the determinant for: | 1 1 1 | | 1 2 3 | | 1 3 6 |.
Step 2: Identify the rows of the matrix: Row 1 is (1, 1, 1), Row 2 is (1, 2, 3), and Row 3 is (1, 3, 6).
Step 3: Check if the rows are linearly dependent. This means that one row can be formed by a combination of the others.
Step 4: Notice that Row 1 can be expressed as a combination of Row 2 and Row 3. Specifically, Row 1 = Row 2 - Row 3 + 1.
Step 5: Since the rows are linearly dependent, the determinant of the matrix is 0.
Determinants – A determinant is a scalar value that can be computed from the elements of a square matrix 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 implies that the determinant is zero.
