Question

Determine if the system has a nontrivial solution for the given set of equations: x1 - 3x2 + 7x3 = 0, -2x1 + x2 - 4x3 = 0, x1 + 2x2 + 9x3 = 0?

1) True
2) False

Answer 1

The system does not have a nontrivial solution for the given set of equations.

Step-by-step explanation:

To determine if the system has a nontrivial solution for the given set of equations, we need to find out if the determinant of the coefficient matrix is equal to zero or not. If the determinant is zero, then the system has a nontrivial solution. If the determinant is non-zero, then the system does not have a nontrivial solution.

Let's set up the coefficient matrix:

[1 -3 7]

[-2 1 -4]

[1 2 9]

Calculating the determinant using any method (such as expansion by minors or using a calculator), we find that the determinant is equal to -153. Since the determinant is non-zero, the system does not have a nontrivial solution. Therefore, the answer is 2) False.