Suppose the vectors x1, x2 and x3 are the solutions of the system of linear - equations, Ax = b when the vector b on the right side is equal to b 1, b 2 and b 3 respectively. If X=[1 1 1],X2[0 2 1],X3=[0 0 1],b1=[1 0 0] b2=[0 2 0] and b3= [0 0 2],then the determinant of A is equal to :

Question

Suppose the vectors x1, x2 and x3 are the solutions of the system of linear - equations, Ax = b when the vector b on the right side is equal to b 1, b 2 and b 3 respectively. If X=[1 1 1],X2[0 2 1],X3=[0 0 1],b1=[1 0 0] b2=[0 2 0] and b3= [0 0 2],then the determinant of A is equal to : (A) (1/2) (B) 4 (C) (3/2) (D) 2

Tardigrade Admin · Accepted Answer

Ax 1= b 1 Ax 2= b 2 Ax 3= b 3 ⇒ |A||1&0&0 1&2&0 1&1&1|=|1&0&0 0&2&0 0&0&2| ⇒ | A |=(4/2)=2

$\frac{1}{2}$

4

$\frac{3}{2}$

2

$A x_{1} = b_{1}$
$A x_{2} = b_{2}$
$A x_{3} = b_{3}$
$\Rightarrow ∣ A ∣ ∣ ∣ 111021001 ∣ ∣ = ∣ ∣ 100020002 ∣ ∣$
$\Rightarrow ∣ A ∣ = \frac{4}{2} = 2$

21​

4

23​

2

Ax1​=b1​ Ax2​=b2​ Ax3​=b3​ ⇒∣A∣∣∣​111​021​001​∣∣​=∣∣​100​020​002​∣∣​ ⇒∣A∣=24​=2

$\frac{1}{2}$

$\frac{3}{2}$

$A x_{1} = b_{1}$
$A x_{2} = b_{2}$
$A x_{3} = b_{3}$
$\Rightarrow ∣ A ∣ ∣ ∣ 111021001 ∣ ∣ = ∣ ∣ 100020002 ∣ ∣$
$\Rightarrow ∣ A ∣ = \frac{4}{2} = 2$