Question

Tìm m để phương trình có 1 nghiệm duy nhất x+2y-2z=2 3x+7y-z=5 2x+4y+mz=7

Answer 1

Rewrite the system of equations in matrix form.

$\begin{bmatrix}1&2&-2\\3&7&-1\\2&4&m\end{bmatrix} \mathbf x = \mathbf b$

This system has a unique solution $\mathbf x = \mathbf A^{-1}\mathbf b$ so long as the inverse of the coefficient matrix $\mathbf A$ exists. This is the case if the determinant is not zero.

We have

$\det(\mathbf A) = m+4$

so the inverse, and hence a unique solution to the system of equations, exists as long as m ≠ -4.