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Exercise 19

Avg difficulty 3.0

  • Solve the system of equations.

    ax+y=a2x+ay=1\begin{array}{rcrcr}ax&+&y&=&a^{2}\\ x&+&ay&=&1\end{array}

    For what values of aa does the system fail to have solutions, and for what values of aa are there infinitely many solutions?

  • Answer the above question for the system.

    ax+y=a3x+ay=1\begin{array}{rcrcr}ax&+&y&=&a^{3}\\ x&+&ay&=&1\end{array}

Hefferon, Linear Algebra, Linear Systems, Describing the Solution Set, Exercise 19

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.