Hello everyone! =)(adsbygoogle = window.adsbygoogle || []).push({});

This might be a good challenge to everyone here... =)

1.) Let A be an n X n matrix and let x and y be vectors in R^n.

Show that Ax .y = x.(A^T)(y), where "." means dot product and T is 'transpose'.

2. show that u.v = (1/4)// u + v //^2 - (1/4)//u - v//^2

where u and v are vectors; "." means dot product and

//.....// denote the length of a vector.

3. Prove the parallelogram law: // u + v //^2 + // u - v //^2 =

2 //u//^2 + 2 //v//^2.

4. Prove the Vandermonde determinant.

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# Prove the parallelogram law

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