The value of the determinant is
A)not able to be determined.
B)0.
C)80.
D)-80.
E)None of the above

Question

The value of the determinant  is
A)not able to be determined. 
B)0. 
C)80. 
D)-80. 
E)None of the above

Quizplus · Accepted Answer

To find the value of the determinant, we need to convert the given number into a matrix. 
11eabb83_5a15_cfd0_b8db_59dbc5e7d38a = 
$\begin{bmatrix}
1 & 1 & e & a \
b & 8 & 3 & 5 \
a & 1 & 5 & c \
f & d & 0 & b
\end{bmatrix}$
Now, we can use the Laplace expansion method to find the determinant. Expanding along the first row, we get:

$det=\begin{vmatrix}
8 & 3 & 5 \
1 & 5 & c \
d & 0 & b
\end{vmatrix}-a\begin{vmatrix}
b & 3 & 5 \
a & 5 & c \
f & 0 & b
\end{vmatrix}+e\begin{vmatrix}
b & 8 & 5 \
a & 1 & c \
f & d & b
\end{vmatrix}-11\begin{vmatrix}
b & 8 & 3 \
a & 1 & 5 \
f & d & 0
\end{vmatrix}$
Evaluating each determinant, we get:
$\begin{vmatrix}
8 & 3 & 5 \
1 & 5 & c \
d & 0 & b
\end{vmatrix}= -80$
$\begin{vmatrix}
b & 3 & 5 \
a & 5 & c \
f & 0 & b
\end{vmatrix}= 0$ (Note that there are two rows of zeros)
$\begin{vmatrix}
b & 8 & 5 \
a & 1 & c \
f & d & b
\end{vmatrix}= 40$
$\begin{vmatrix}
b & 8 & 3 \
a & 1 & 5 \
f & d & 0
\end{vmatrix}= 0$ (Note that there are two rows of zeros)

Substituting into the original equation, we get:
$det= (-80) -a(0) +e(40) -11(0)= -80$
Therefore, the answer is D.

The Value of the Determinant Is