Find the Determinant [[1,24,4],[3,50,8],[3,48,6]]

Problem

det(1)

Solution

1. Set up the determinant expansion using the first row.

det(A)=(a_11)*((a_22)*(a_33)−(a_23)*(a_32))−(a_12)*((a_21)*(a_33)−(a_23)*(a_31))+(a_13)*((a_21)*(a_32)−(a_22)*(a_31))

2. Substitute the values from the matrix into the expansion formula.

det(A)=1*(50⋅6−8⋅48)−24*(3⋅6−8⋅3)+4*(3⋅48−50⋅3)

3. Calculate the products inside the parentheses.

det(A)=1*(300−384)−24*(18−24)+4*(144−150)

4. Simplify the terms inside the parentheses.

det(A)=1*(−84)−24*(−6)+4*(−6)

5. Multiply the coefficients by the simplified terms.

det(A)=−84+144−24

6. Sum the results to find the final value.

det(A)=36

Final Answer

det(1)=36

Want more problems? Check here!