Find the Determinant [[6,6,6],[6,65,4],[1,21,6]]

Problem

det(6)

Solution

1. Identify the matrix and the method for calculating the determinant. We will use expansion by minors along the first row.

2. Set up the expansion using the elements of the first row: (a_11)=6 (a_12)=6 and (a_13)=6

3. Calculate the first term by multiplying (a_11) by the determinant of its 2×2 minor.

6⋅det(65)=6*(65⋅6−4⋅21)

6*(390−84)=6*(306)=1836

4. Calculate the second term by multiplying −(a_12) by the determinant of its 2×2 minor.

−6⋅det(6)=−6*(6⋅6−4⋅1)

−6*(36−4)=−6*(32)=−192

5. Calculate the third term by multiplying (a_13) by the determinant of its 2×2 minor.

6⋅det(6)=6*(6⋅21−65⋅1)

6*(126−65)=6*(61)=366

6. Sum the results of the three terms to find the final determinant.

1836−192+366=2010

Final Answer

det(6)=2010

Want more problems? Check here!