The system of linear equations given is:

1) x + 2y - 3z = a
2) 2x + 6y - 11z = b
3) x - 2y + 7z = c

This system of equations will have at least one solution if the determinant of the coefficients of the variables is not equal to zero. The determinant of the coefficients is calculated as follows:

| 1 2 -3 |
| 2 6 -11|
| 1 -2 7 |

The determinant of this matrix is:

1*(6*7 - (-11)*(-2)) - 2*(2*7 - (-11)*1) + 3*(2*(-2) - 6*1) = 1*(42 - 22) - 2*(14 + 11) + 3*(-4 - 6) = 20 - 50 - 30 = -60.

So, the system of equations will have at least one solution if -60 ≠ 0, which is always true. Therefore, the system of equations will always have at least one solution, regardless of the values of a, b, and c.

Question

The system of linear equations given is:

1) x + 2y - 3z = a
2) 2x + 6y - 11z = b
3) x - 2y + 7z = c

This system of equations will have at least one solution if the determinant of the coefficients of the variables is not equal to zero. The determinant of the coefficients is calculated as follows:

| 1  2 -3 |
| 2  6 -11|
| 1 -2  7 |

The determinant of this matrix is:

1*(6*7 - (-11)*(-2)) - 2*(2*7 - (-11)*1) + 3*(2*(-2) - 6*1) = 1*(42 - 22) - 2*(14 + 11) + 3*(-4 - 6) = 20 - 50 - 30 = -60.

So, the system of equations will have at least one solution if -60 ≠ 0, which is always true. Therefore, the system of equations will always have at least one solution, regardless of the values of a, b, and c.

Knowee AI · Accepted Answer

The system of linear equations given is:

1) x + 2y - 3z = a
2) 2x + 6y - 11z = b
3) x - 2y + 7z = c

This system of equations will have at least one solution if the determinant of the coefficients of the variables is not equal to zero. The determinant of the coefficients is calculated as follows:

| 1  2 -3 |
| 2  6 -11|
| 1 -2  7 |

The determinant of this matrix is:

1*(6*7 - (-11)*(-2)) - 2*(2*7 - (-11)*1) + 3*(2*(-2) - 6*1) = 1*(42 - 22) - 2*(14 + 11) + 3*(-4 - 6) = 20 - 50 - 30 = -60.

So, the system of equations will have at least one solution if -60 ≠ 0, which is always true. Therefore, the system of equations will always have at least one solution, regardless of the values of a, b, and c.

Consider the following system of linear equations,x + 2y − 3z = a2x + 6y − 11z = bx − 2y + 7z = cwhere a, b and c are real constants. Find the condition for a, b and c such that this system of linear equationshas at least one solution

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