Suppose the vectors x 1 , x 2 and x 3 are the solutions of the system of linear equations, A x = 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 1 , x 2 = 0 2 1 , x 3 = 0 0 1 ; b 1 = 1 0 0 , b 2 = 0 2 0 , b 3 = 0 0 2 , then the determinant of A is equal to

Step-by-step solution

Let A = α 1 α 2 α 3 β 1 β 2 β 3 γ 1 γ 2 γ 3 . Now satisfying x 1 ,   x 2 ,   x 3 in A x = b A x 1 = b 1 ⇒ α 1 α 2 α 3 β 1 β 2 β 3 γ 1 γ 2 γ 3 1 1 1 = 1 0 0 ⇒ α 1 + α 2 + α 3 = 1 β 1 + β 2 + β 3 = 0 γ 1 + γ 2 + γ 3 = 0 …   i Now A x 2 = b 2 ⇒ α 1 α 2 α 3 β 1 β 2 β 3 γ 1 γ 2 γ 3 0 2 1 = 0 2 0 ⇒ 2