Step 1: Understand what a determinant is. It is a special number that can be calculated from a square matrix.
Step 2: Identify the matrix given in the question: | 1 2 3 | | 4 5 6 | | 7 8 9 |.
Step 3: Recognize that the matrix has 3 rows and 3 columns, making it a 3x3 matrix.
Step 4: Check if the rows of the matrix are linearly dependent. This means that one row can be formed by a combination of the others.
Step 5: Notice that the third row (7, 8, 9) can be formed by adding the first row (1, 2, 3) and the second row (4, 5, 6).
Step 6: Since the rows are linearly dependent, the determinant of this 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 results in a determinant of zero.
