Math  /  Algebra

QuestionDo the planes x1+4x2+x3=5x_{1}+4 x_{2}+x_{3}=5, x2x3=1x_{2}-x_{3}=1, and 2x1+10x2=82 x_{1}+10 x_{2}=8 intersect at a common point? A, B, or C?

Studdy Solution
The third row of the matrix is now all zeros, which means that the system of equations is dependent. This implies that the three planes intersect along a line, and thus have infinitely many points of intersection.
Therefore, the correct answer is A. The three planes have at least one common point of intersection.

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