If J = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], what is det(J)?

If J = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], what is det(J)?

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 J. J is a 3x3 matrix: [[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 formed by adding or scaling the others.
Step 4: 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 5: Since the rows are linearly dependent, the determinant of the matrix J 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 affects the determinant.