Find the Determinant [[2,9,4],[37,-6,23],[14,4,6]]

Problem

det(2)

Solution

1. Apply the expansion formula for a 3×3 determinant along the first row.

D=(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.

D=2*((−6)*(6)−(23)*(4))−9*((37)*(6)−(23)*(14))+4*((37)*(4)−(−6)*(14))

3. Calculate the products inside the parentheses for the first term.

2*(−36−92)=2*(−128)=−256

4. Calculate the products inside the parentheses for the second term.

−9*(222−322)=−9*(−100)=900

5. Calculate the products inside the parentheses for the third term.

4*(148−(−84))=4*(148+84)=4*(232)=928

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

−256+900+928=1572

Final Answer

det(2)=1572

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