Step 1: Identify the matrix I, which is [[1, 2], [2, 4]].
Step 2: Understand that the determinant of a 2x2 matrix [[a, b], [c, d]] is calculated using the formula: det(I) = a*d - b*c.
Step 3: In our matrix, a = 1, b = 2, c = 2, and d = 4.
Step 4: Plug the values into the formula: det(I) = (1 * 4) - (2 * 2).
Step 5: Calculate the result: det(I) = 4 - 4 = 0.
Step 6: Conclude that the determinant is 0, which indicates that the rows of the matrix are linearly dependent.
Determinant – 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.
