In our last class, we introduced Gaussian elimination. Today, we’ll examine circumstances where this process might break down. A crucial aspect of our previous example was that every pivot was nonzero, but this isn’t always true for all matrices. To illustrate how we handle these challenging situations, let’s consider the...
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Two lines in general positions typically intersect at a point. Only in specific cases—when lines are parallel or overlapping—does this intersection not occur. This concept explains why we call a system of $n$ equations in $n$ unknowns nonsingular when it has a unique solution, and singular otherwise.
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Under what condition on $y_1$ , $y_2$ , $y_3$ do the points $(0, y_1 )$, $(1, y_2 )$,
$(2, y_3 )$ lie on a straight line?
Use elimination to solve
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