Find the value of the determinant.
-$$\left| \begin{array} { l l l }
3 & 5 & 5 \
6 & 3 & 2 \
1 & 1 & 5
\end{array} \right|$$
A) -106
B) 256
C) -86
D) 86

Question

Find the value of the determinant.
-$$\left| \begin{array} { l l l } 
3 & 5 & 5 \
6 & 3 & 2 \
1 & 1 & 5
\end{array} \right|$$
A) -106
B) 256
C) -86
D) 86

Quizplus · Accepted Answer

To find the determinant of the given $3 \times 3$ matrix, we use the formula for the determinant of a $3 \times 3$ matrix: $$ \text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg) $$ where $a, b, c, d, e, f, g, h, i$ are the elements of the matrix arranged as follows: $$ \left| \begin{array} { c c c } a & b & c \ d & e & f \ g & h & i \end{array} \right| $$ Substituting the given values, we get: $$ \text{det}(A) = 3(3 \cdot 5 - 2 \cdot 1) - 5(6 \cdot 5 - 2 \cdot 1) + 5(6 \cdot 1 - 3 \cdot 1) $$ $$ \text{det}(A) = 3(15 - 2) - 5(30 - 2) + 5(6 - 3) $$ $$ \text{det}(A) = 3(13) - 5(28) + 5(3) $$ $$ \text{det}(A) = 39 - 140 + 15 $$ $$ \text{det}(A) = -86 $$

Find the Value of the Determinant ∣355632115∣\left| \begin{array} { l l l } 3 & 5 & 5 \\6 & 3 & 2 \\1 & 1 & 5\end{array} \right|​361​531​525​​

Find the Value of the Determinant $\left| \begin{array} { l l l } 3 & 5 & 5 \\6 & 3 & 2 \\1 & 1 & 5\end{array} \right|$