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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 b1, b2 and b3 respectively. If x1 = [1, 1, 1]^T, x2 = [0, 2, 1]^T, x3 = [0, 0, 1]^T, b1 = [1, 0, 0]^T, b2 = [0, 2, 0]^T and b3 = [0, 0, 2]^T, then the determinant of A is equal to:

1. 1/2
2. 4
3. 2
4. 3/2

Correct answer: 2

Solution

The determinant of matrix A can be calculated using the vectors x1, x2, and x3 as they represent the solutions to the system of equations. The volume of the parallelepiped formed by these vectors in three-dimensional space is given by the absolute value of the determinant, which in this case is 2, indicating that the vectors are linearly independent and span a volume of 2.

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