Step 2: Understand that the determinant is a value that can tell us about the matrix's properties.
Step 3: Check if the rows of the matrix are linearly dependent. This means that one row can be made by adding or multiplying the other rows.
Step 4: Notice that each row is a multiple of the others. For example, the second row (2, 2, 2) is 2 times the first row (1, 1, 1), and the third row (3, 3, 3) is 3 times the first row.
Step 5: Since the rows are linearly dependent, the determinant of the matrix is 0.
Determinant of a Matrix – The 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.
