Answer:
(1, A), (2, B), (3, D), (4, C)
Step-by-step explanation:
In the above answer pairs, we have numbered the systems of equations 1–4 from left to right, and the diagrams A–D from top to bottom.
The attachments show the row-reduction of the first three systems (1–3). The last system (4) is obviously three repetitions of the same equation, so is the same plane 3 times, as in diagram C.
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1. The last row of the reduced matrix has a non-zero element in the rightmost column, indicating there is no solution. The two non-zero rows indicate the system specifies planes that intersect in parallel lines. In a local area, the solution sort of matches diagram A in that one plane intersects the two others in parallel lines. Though the lines are parallel, the planes are not.
The last attachment shows a rendering of the first system of equations. Though the colors leave something to be desired, you can see that they intersect in a way that creates a triangular tunnel. No (x, y, z) value is found on all three planes.
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2. The reduced matrix shows there is a single solution, corresponding to the planes all intersecting at one point.
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3. The last row of the reduced matrix being all zeros means the solution is a line, as shown in diagram D.
