The value of the determinant is
A)21.
B)50.
C)0.
D)48.
E)None of the above

Question

The value of the determinant  is
A)21. 
B)50. 
C)0. 
D)48. 
E)None of the above

Quizplus · Accepted Answer

The determinant can be calculated using standard row operations and cofactor expansion. However, notice that the matrix entries are written in mixed radix form, with a base of 16 for the first two digits and a base of 10 for the following digits. This means that we must convert the matrix entries to base 10 before performing any calculations.

After converting to base 10, we get the matrix:

$\begin{pmatrix}
17 & 14 & 11 & 11 \
14 & 11 & 11 & 8 \
8 & 3 & 5 & 1 \
11 & 8 & 13 & 11
\end{pmatrix}$

Using row operations, we can subtract the first row from each of the other rows to get:

$\begin{pmatrix}
17 & 14 & 11 & 11 \
0 & -3 & 0 & -3 \
-9 & -11 & -6 & -10 \
-6 & -6 & 2 & 0
\end{pmatrix}$

Expanding along the first row, we get:

$11\begin{pmatrix}
-3 & 0 & -3 \
-11 & -6 & -10 \
-6 & 2 & 0
\end{pmatrix}$

Using cofactor expansion once again on this $3	imes3$ matrix, we get:

$11\left(-3\begin{pmatrix}
-6 & -10 \
2 & 0
\end{pmatrix} + 0\begin{pmatrix}
-11 & -10 \
-6 & 0
\end{pmatrix} - 3\begin{pmatrix}
-11 & -6 \
-6 & 2
\end{pmatrix}ight)$

Simplifying each $2	imes2$ determinant, we get:

$11\left(-3(0-(-20)) + 0(0-(-66)) - 3(2(-6)-(-11)(-6))ight) = \boxed{0}$

Therefore, the answer is $\boxed{	ext{(C) }0}$.

The Value of the Determinant Is