The value of the determinant is
A)not able to be determined.
B)0.
C)80.
D)-80.

Question

The value of the determinant  is
A)not able to be determined. 
B)0. 
C)80. 
D)-80.

Quizplus · Accepted Answer

The determinant of a 3x3 matrix can be found using the formula:
det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)
In this case, the matrix can be written as:

| 1 1 ea |
| a 1 b  |
| 9 e5 81 |

Using the above formula, we get:

det(A) = 1(1*81 - e5*b) - 1(a*81 - ea*9) + ea(a*e5 - 1*9)
       = 81 - e5b - 81a + 9ea + e5a - ea*9
       = e5a - ea*9 - e5b
       = e5(a - b - 9e)

As we can see, the value of the determinant depends on the value of (a - b - 9e). Therefore, we cannot determine the value of the determinant without knowing the values of a, b, and e. However, we can see that the answer cannot be A or C as they give a specific value for the determinant. 
Now, if we take the values a=1, b=2, and e=3, we get (a - b - 9e) = 1 - 2 - 27 = -28. Substituting this in the above expression, we get:

det(A) = e5(-28) = -140

Therefore, the correct answer is D.

The Value of the Determinant Is