Find the Determinant [[6,3],[-2,8]]

Problem

det(6)

Solution

1. Identify the formula for the determinant of a 2×2 matrix [[a,b],[c,d]] which is a*d−b*c

2. Assign the values from the given matrix: a=6 b=3 c=−2 and d=8

3. Substitute these values into the determinant formula.

det(6)=(6)*(8)−(3)*(−2)

4. Multiply the terms to find the products.

(6)*(8)=48

(3)*(−2)=−6

5. Subtract the products, taking care with the signs.

48−(−6)=48+6

6. Simplify the final result.

48+6=54

Final Answer

det(6)=54

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