Suppose the vectors x<sub>1</sub>, x<sub>2</sub> and x<sub>3</sub> are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b<sub>1</sub>, b<sub>2</sub> and b<sub>3</sub> respectively. If x<sub>1</sub> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[
Step-by-Step Solution
Key Concept: The system of equations can be written as AX = B, where X = [x1 x2 x3] and B = [b1 b2 b3]. Thus, det(A) * det(X) = det(B).
Let X = [x1 x2 x3] = [[1, 0, 0], [1, 1, 0], [1, 1, 1]] and B = [b1 b2 b3] = [[1, 0, 0], [0, 2, 0], [0, 0, 2]]. Since AX = B, det(A)det(X) = det(B). det(X) = 1(1*1 - 0*1) = 1. det(B) = 1(2*2 - 0*0) = 4. Therefore, det(A) * 1 = 4, so det(A) = 4.
Correct Answer: 4