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An Analogy with Regular Algebra

As we saw in the video, solving matrix-vector equations is as simple as multiplying both sides of the equation by \(A\)'s inverse, \(A^{-1}\), should it exist. The analogy with solving linear equations like \(5x = 7\) is a good one.

If \(A^{-1}\) doesn't exist, this does not work. The equivalent analogy for linear equations would be a situation in which the coefficient in front of the \(x\) were \(0\), which is the only real number that does not have an inverse. Which of the following does NOT analogize in this situation?

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