Find the Determinant (3)[[260,1,1],[255,3,0],[435,1,4]]

Problem

3⋅det(260)

Solution

1. Identify the matrix and the scalar multiplier. We need to calculate the determinant of the 3×3 matrix and then multiply the result by 3

2. Expand the determinant along the second row to take advantage of the zero. The formula for the determinant of a matrix A using the second row is |A|=(a_21)*(C_21)+(a_22)*(C_22)+(a_23)*(C_23)

3. Calculate the cofactor (C_21) This involves the minor formed by removing row 2 and column 1.

(C_21)=−1⋅det(1)

(C_21)=−1⋅(1⋅4−1⋅1)

(C_21)=−3

4. Calculate the cofactor (C_22) This involves the minor formed by removing row 2 and column 2.

(C_22)=1⋅det(260)

(C_22)=1⋅(260⋅4−1⋅435)

(C_22)=1040−435

(C_22)=605

5. Calculate the cofactor (C_23) Since (a_23)=0 the value of (a_23)*(C_23) is 0

6. Sum the products to find the determinant of the matrix.

det(A)=255⋅(−3)+3⋅605+0

det(A)=−765+1815

det(A)=1050

7. Multiply the determinant by the scalar 3

3⋅1050=3150

Final Answer

3⋅det(260)=3150

Want more problems? Check here!