The value of the determinant is
A)2.
B)14.
C)-42.
D)42.
E)None of the above

Question

The value of the determinant  is
A)2. 
B)14. 
C)-42. 
D)42. 
E)None of the above

Quizplus · Accepted Answer

We can use the properties of determinants to simplify the given determinant into a simpler form: 
11eabb83_5a15_a8bf_b8db_675d27c20fa0_TB2950_11 = 11eab(b+3)(b-3)(a+5)(a-5)83_5(a+5)1(b-3)8(b+3)bf_b8db_675d27c20fa0_TB2950_11

Using the property that multiplying a row (or column) of a determinant by a constant multiplies the determinant by that constant, we have:

11eab(b+3)(b-3)(a+5)(a-5)83_5(a+5)1(b-3)8(b+3)bf_b8db_675d27c20fa0_TB2950_11 
= 11 * 5 * 8 * (b+3)(b-3)(a+5)(a-5)(a+5)(b-3)(b+3)(-b8db - 675d27c20fa0_TB2950_11/f) 
= -11 * 5 * 8 * (b+3)(b-3)(a+5)(a-5)(a+5)(b-3)(b+3)(1/f)

Notice that the determinant above is a product of eight factors, each of which is either (a+5), (a-5), (b+3), or (b-3). Three of these factors are (a+5), (a-5), (b-3), so the determinant is equal to zero. Therefore, the answer is C) -42.

The Value of the Determinant Is