If E = [[a, b], [c, d]], what is the expression for det(E)? (2023)

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Q: If E = [[a, b], [c, d]], what is the expression for det(E)? (2023)

Solution: The determinant of E is calculated as (a*d) - (b*c) = ad - bc.

Steps: 5

Step 1: Identify the elements of the matrix E. The matrix E is given as [[a, b], [c, d]]. This means a is in the first row and first column, b is in the first row and second column, c is in the second row and first column, and d is in the second row and second column.
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is det(E) = (first element * second element of the opposite diagonal) - (second element * first element of the opposite diagonal).
Step 3: Apply the formula to the elements of matrix E. Here, the first element is 'a' and the second element of the opposite diagonal is 'd'. The second element is 'b' and the first element of the opposite diagonal is 'c'.
Step 4: Substitute the elements into the formula: det(E) = (a * d) - (b * c).
Step 5: Simplify the expression to get the final result: det(E) = ad - bc.