If A and B are both invertible square matrices of the same size with complex entries, there exists a complex scalar c such that A+cB is noninvertible.(adsbygoogle = window.adsbygoogle || []).push({});

I know this to be true, but I can't prove it. I tried working with determinants, but a specific selection of c can only get rid of one entry in A+cB, which is not enough since the matrices do not have to be triangular. How would one go about proving this theorem?

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# Sum A+cB of invertible matrices noninvertible?

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