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Science Through Time
What Is A Basis In A Vector Space? - Science Through Time
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![Prove that |[1 +a^2 -b^2, 2ab, -2b],[2ab, 1-a^2 +b^2, 2a],[2b, -2a, 1-a^2 -b^2]| = (1 + a^2 + b^2)^3](http://i.ytimg.com/vi/B7UwIYXEcX8/mqdefault.jpg "Prove that |[1 +a^2 -b^2, 2ab, -2b],[2ab, 1-a^2 +b^2, 2a],[2b, -2a, 1-a^2 -b^2]| = (1 + a^2 + b^2)^3")
![Prove that |[b^2 + c^2, a^2, a^2],[b^2, c^2 + a^2, b^2],[c^2, c^2, a^2 + b^2]| = 4a^2 b^2 c^2](http://i.ytimg.com/vi/IG15iLK0PtI/mqdefault.jpg "Prove that |[b^2 + c^2, a^2, a^2],[b^2, c^2 + a^2, b^2],[c^2, c^2, a^2 + b^2]| = 4a^2 b^2 c^2")
![Prove that |[a - b - c, 2a, 2a],[2b, b - c - a, 2b],[2c, 2c, c - a - b]| = (a + b +c)^3](http://i.ytimg.com/vi/F6Kll3fQIB0/mqdefault.jpg "Prove that |[a - b - c, 2a, 2a],[2b, b - c - a, 2b],[2c, 2c, c - a - b]| = (a + b +c)^3")
![If A = [[-1],[2],[3]], B=[-2,-1,-4], verify that (AB)' = B'A'.](http://i.ytimg.com/vi/QYPtuaZvwfA/mqdefault.jpg "If A = [[-1],[2],[3]], B=[-2,-1,-4], verify that (AB)' = B'A'.")
