Let A be the original matrix given in Exercise 16, and let Notice that A, B, and
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Notice that A, B, and C are nearly the same except that the first column of A equals the sum of the first columns of B and C. A linearity property of the determinant function, discussed in Section 3.2, says that det A = det B C det C. Use this fact to prove the formula in Exercise 16 by induction on the size of matrix A?
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First consider the case n 2 In this case So det A det B det C aa b ab b 2 a ...View the full answer
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