Question: hey everyone got this as an assignment question and i...
Got this as an assignment question and I honestly have no idea where to start. If someone could point me in the right direction, that would be great.
A Pythagorean triple (a, b, c) consists of positive integers a, b and c satisfying a < b < c and a ^2 + b ^2 = c ^2 . They correspond to right-angled triangles whose sides have whole number lengths. The simplest and most well-known example is (3, 4, 5).
(a) Let (a, b, c) be a Pythagorean triple and let P = . Verify that P has all the following properties:
A: All entries of P are positive integers.
B: P is symmetric (this means P^T = P).
C: det P = 0.
D: p11 − p22 = 2k for some integer k > p12 (pij is the i, j−th entry of P.)
(b) Conversely, verify that if a 2×2 matrix P has properties A–D then P = for a suitable Pythagorean triple (a, b, c).
Thanks in advance!