Question

Answer the questions in pic​

Answer 1

(a) Find the determinant :

$\qquad\dashrightarrow~ \left[\begin{array}{ccc}9&2&8\\5&6&7\\1&3&4\\\end{array}\right]$

$\qquad\sf\dashrightarrow~ Determinant=a(ei-fh)-b(di-fg)+c(dh-eg)$

$\qquad\sf \dashrightarrow ~det(A)=9[(6)(4)-(7)(3)]-2[(5)(4)-(7)(1)]+8[(5)(3)-(6)(1)]$

$\qquad\sf\dashrightarrow~ det(A)=9[24-21]-2[20-7]+8[15-6]$

$\qquad\sf\dashrightarrow ~ det(A)=9[3]-2[13]+8[9]$

$\qquad\sf \dashrightarrow ~ det(A)=27-26+72$

$\qquad\bf \dashrightarrow~ det(A)=73$

(b) Find the value of x :

$\qquad\dashrightarrow~ \left[\begin{array}{cc}2x&1\\5&0\\\end{array}\right]=\left[\begin{array}{cc}6x&2\\3&4\\\end{array}\right]$

$\sf \qquad\dashrightarrow~ Determinant=ad-bc$

$\sf \qquad\dashrightarrow~ 2x(0)-1(5)=6x(4)-2(3)$

$\sf \qquad \dashrightarrow \: 0 - 5 = 24x - 6$

$\sf \qquad \dashrightarrow \: 24x - 6 + 5 = 0$

$\sf \qquad \dashrightarrow \: 24x = 1$

$\bf \qquad \dashrightarrow \: x = \dfrac{1}{24 }$

(c) Find the determinant :

$\qquad\dashrightarrow~ \left[\begin{array}{ccc}0&6&0\\1&2&3\\5&6&7\\\end{array}\right]$

$\sf \qquad\dashrightarrow~ Determinant=a(ei-fh)-b(di-fg)+c(dh-eg)$

$\sf\qquad\dashrightarrow~ det(A)=0[(2)(7)-(3)(6)]-6[(1)(7)-(3)(5)]+0[(1)(6)-(2)(5)]$

$\sf\qquad\dashrightarrow~ det(A)=0[14-8]-6[7-15]+0[6-10]$

$\sf\qquad\dashrightarrow~ det(A)=0-6[-8]+0$

$\bf\qquad\dashrightarrow~ det(A)=48$