Question

find the value of the determinant 7/3 5/3 3/2 1//2

Answer 1

The value of the determinant 7/3 5/3 3/2 1/2

Answer 2

$\displaystyle\begin{vmatrix} \dfrac{7}{3} & \dfrac{5}{3} \\ \\ \dfrac{3}{2} & \dfrac{1}{2} \end{vmatrix} = - \frac{4}{3}$

Given :

$\displaystyle\begin{vmatrix} \dfrac{7}{3} & \dfrac{5}{3} \\ \\ \dfrac{3}{2} & \dfrac{1}{2} \end{vmatrix}$

To find :

The value of the determinant

Solution :

Step 1 of 2 :

Write down the given determinant

Here the given determinant is

$\displaystyle\begin{vmatrix} \dfrac{7}{3} & \dfrac{5}{3} \\ \\ \dfrac{3}{2} & \dfrac{1}{2} \end{vmatrix}$

Step 2 of 2 :

Find the value of the determinant

$\displaystyle\begin{vmatrix} \dfrac{7}{3} & \dfrac{5}{3} \\ \\ \dfrac{3}{2} & \dfrac{1}{2} \end{vmatrix}$

$\displaystyle \sf{ = \bigg( \frac{7}{3} \times \frac{1}{2} \bigg) - \bigg( \frac{5}{3} \times \frac{3}{2} \bigg)}$

$\displaystyle \sf{ = \frac{7}{6} - \frac{15}{6} }$

$\displaystyle \sf{ = \frac{7 - 15}{6} }$

$\displaystyle \sf{ = \frac{ - 8}{6} }$

$\displaystyle \sf{ = - \frac{8}{6} }$

$\displaystyle \sf{ = - \frac{4}{3} }$

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