Find the determinant of the matrix $\left[ \begin{array} { r r }
\frac { 1 } { 2 } & 1 \\
- \frac { 1 } { 2 } & \frac { 3 } { 2 }
\end{array} \right]$ , if it exists
A) $\frac { 3 } { 4 }$
B) $5$
C) $- \frac { 5 } { 4 }$
D) $\frac { 1 } { 4 }$
E) $\frac { 5 } { 4 }$

Question

Find the determinant of the matrix $\left[ \begin{array} { r r } 
\frac { 1 } { 2 } & 1 \\
- \frac { 1 } { 2 } & \frac { 3 } { 2 }
\end{array} \right]$ , if it exists
A) $\frac { 3 } { 4 }$
B) $5$
C) $- \frac { 5 } { 4 }$
D) $\frac { 1 } { 4 }$
E) $\frac { 5 } { 4 }$

Quizplus · Accepted Answer

The determinant of a 2x2 matrix $\left[ \begin{array} { r r } a & b \ c & d \end{array} \right]$ is calculated as $ad - bc$. For the given matrix, $a = \frac{1}{2}$, $b = 1$, $c = -\frac{1}{2}$, and $d = \frac{3}{2}$. Thus, the determinant is $\frac{1}{2} \cdot \frac{3}{2} - 1 \cdot (-\frac{1}{2}) = \frac{3}{4} + \frac{1}{2} = \frac{5}{4}$.

Find the Determinant of the Matrix [121−1232]\left[ \begin{array} { r r } \frac { 1 } { 2 } & 1 \\\\- \frac { 1 } { 2 } & \frac { 3 } { 2 }\end{array} \right]​21​−21​​123​​​

Find the Determinant of the Matrix $\left[ \begin{array} { r r } \frac { 1 } { 2 } & 1 \\\\- \frac { 1 } { 2 } & \frac { 3 } { 2 }\end{array} \right]$