Find inner product generated by a matrix

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Q. Let ⟨u,v⟩ be the inner product on R2 generated by A= ... , and let u=(−2,−1) and v=(4,7). Find ⟨u,v⟩.

What you'll need:

⟨u,v⟩=v^T A^T Au

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what happens if the matrix is not invertible

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