Step 1: Identify the matrix for which we want to find the determinant. The matrix is: [[1, 2], [3, 4], [5, 6]].
Step 2: Note that this matrix has 3 rows and 2 columns, which means it is not a square matrix.
Step 3: Understand that only square matrices (same number of rows and columns) have a determinant.
Step 4: Since the matrix is not square, we cannot calculate a determinant in the traditional sense.
Step 5: However, we can observe that the rows of the matrix are linearly dependent, meaning one row can be expressed as a combination of the others.
Step 6: Because the rows are linearly dependent, we conclude that the determinant 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.
