Find the determinant of E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. (2019)

Find the determinant of E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. (2019)

Step 1: Understand what a determinant is. The determinant is a special number that can be calculated from a square matrix.
Step 2: Identify the matrix E. The matrix E is given as [[1, 2, 3], [4, 5, 6], [7, 8, 9]].
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 if you add the first row [1, 2, 3] and the second row [4, 5, 6], you get [5, 7, 9], which is not equal to the third row [7, 8, 9]. However, if you look closely, you can see that the third row can be formed by a combination of the first two rows.
Step 5: Since the rows are linearly dependent, the determinant of the matrix E is 0.
Step 6: Conclude that the determinant of E 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.