Step 2: Identify the rows of the matrix: Row 1 is [1, 1, 1], Row 2 is [2, 2, 2], and Row 3 is [3, 3, 3].
Step 3: Check if the rows are linearly dependent. This means that one row can be made by adding or multiplying the others.
Step 4: Notice that Row 2 is just Row 1 multiplied by 2, and Row 3 is Row 1 multiplied by 3.
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 the others, which results in a determinant of zero.
