The correct determinant value for the determinant would be
A)(8)(4)(3)(6).
B)(8)(4)+ (3)(6).
C)(8)(4)- (3)(6).
D)(8)(3)- (6)(4).
E)(8)(6)- (3)(4).

Question

The correct determinant value for the determinant  would be
A)(8)(4)(3)(6). 
B)(8)(4)+ (3)(6). 
C)(8)(4)- (3)(6). 
D)(8)(3)- (6)(4). 
E)(8)(6)- (3)(4).

Quizplus · Accepted Answer

The determinant value can be calculated by taking the sum of the products of each element in the rows/columns multiplied by its corresponding cofactor. The cofactor for the first element (11) is (-1)^(1+1) = 1 and its corresponding 2x2 minor is ea-1b. The cofactor for the second element (ea) is (-1)^(1+2) = -1 and its corresponding 2x2 minor is ab-3. The cofactor for the third element (bb) is (-1)^(1+3) = 1 and its corresponding 2x2 minor is ae-1d. The cofactor for the fourth element (83) is (-1)^(1+4) = -1 and its corresponding 2x2 minor is ad-bd. The cofactor for the fifth element (5a14) is (-1)^(1+5) = 1 and its corresponding 2x2 minor is 11d-bbdb. The cofactor for the sixth element (21f2) is (-1)^(1+6) = -1 and its corresponding 2x2 minor is 11b-3bb. The cofactor for the seventh element (b8db) is (-1)^(1+7) = 1 and its corresponding 2x2 minor is 11e-ae5. The cofactor for the eighth element (1d468ecf4bd9) is (-1)^(1+8) = -1 and its corresponding 2x2 minor is 11a-ea5. The cofactor for the ninth element (TB2950) is (-1)^(1+9) = 1 and its corresponding 2x2 minor is eb-3a. The cofactor for the tenth element (11) is (-1)^(1+10) = -1 and its corresponding 2x2 minor is ab-83. Thus, the determinant value is (11)(ea-1b)(bb)(83)(5a14)(21f2)(b8db)(1d468ecf4bd9)(TB2950)(11) = (11)((ea)(bb)-(1b)(ab))-(83)((5a14)(b8db)-(1d468ecf4bd9)(21f2))+(TB2950)((11)(ad-bd)-(83)(11d-bbdb)+(5a14)(11b-3bb)) = (11)((ea)(bb)-(1b)(ab))+(83)((1d468ecf4bd9)(21f2)-(5a14)(b8db))+(TB2950)((ab-83)(11)) = (8)(4)-(3)(6) = 18. Therefore, the correct choice is C.

The Correct Determinant Value for the Determinant Would Be