MathAlgebraLinear algebraSystems of linear equations

Solving linear systems using the Gauss elimination

Theory

Determining the number of solutions

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Examine the system

{x−y+2z+2w=23x−2y−z−w=−15x−3y−4z−2w=−17x−4y−7z−5w=−7\begin{cases} x- y + 2z + 2w= 2\\ 3x-2y-z-w= -1\\ 5x-3y-4z - 2w = -1\\ 7x-4y-7z - 5w = -7 \end{cases}

If there is only one solution, write the values of x,y,z,wx, y, z, w, divided by spaces. If there are no solutions, write 0, and if there are infinite solutions, write -1.

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