Question

solve it step by step​

Answer 1

GIVEN :–

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

TO FIND :–

• Determinant = ?

SOLUTION :–

• Let –

$\\ \implies \sf A = \begin{bmatrix} \dfrac{7}{3}& \dfrac{5}{3} \\ \\ \dfrac{3}{2} &\dfrac{1}{2} \end{bmatrix}$

$\\ \rule{220}{2}$

• We know that If –

$\\ \implies \sf A = \begin{bmatrix}a& b \\ \\ c &d \end{bmatrix}$

• Then Determinant of 'A' –

$\\ \implies \sf | A | =ad - bc$

$\\ \rule{220}{2}$

• Now Applying –

$\\ \implies \sf |A| = \dfrac{7}{3} \times\dfrac{1}{2} - \dfrac{5}{3} \times \dfrac{3}{2}$

$\\ \implies \sf |A| = \dfrac{7}{6} - \dfrac{15}{6}$

$\\ \implies \sf |A| = \dfrac{7 - 15}{6}$

$\\ \implies \sf | A| = - \dfrac{ 8}{6}$

$\\ \implies \large{ \boxed{ \sf | A| = - \dfrac{4}{3}}}$

Answer 2

Step-by-step explanation:

D= 7/3×1/2-5/3×3/2

= 7/6-15/6

= -8/6

= -4/3

Ans: Determinant= -4/3