- #1
johndoe3344
- 29
- 0
Find an orthogonal transformation T from R3 to R3 such that
T of the column vector [2/3 2/3 1/3] is equal to the column vector [0 0 1]
So I tried to construct out the 3x3 matrix
[a b c]
[d e f]
[g h i]
and applied the properties of an orthogonal matrix and basic algebra. I ended up with a giant mess of equations without any way to solve them... for example..
(2/3)a + (2/3)b + (1/3)c = 0
...
a^2 + d^2 + g^2 = 1
...
ab + de + gh = 0
...
and so on.
Could anyone shed some light on how to approach these types of problems?
T of the column vector [2/3 2/3 1/3] is equal to the column vector [0 0 1]
So I tried to construct out the 3x3 matrix
[a b c]
[d e f]
[g h i]
and applied the properties of an orthogonal matrix and basic algebra. I ended up with a giant mess of equations without any way to solve them... for example..
(2/3)a + (2/3)b + (1/3)c = 0
...
a^2 + d^2 + g^2 = 1
...
ab + de + gh = 0
...
and so on.
Could anyone shed some light on how to approach these types of problems?