- #1
Physicsissuef
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Homework Statement
Let's say that V is the vector space of all antisymmetric 3x3 matrices. Find the coordinates of the matrix [tex]A=\begin{bmatrix}
0 & 1 & -2\\
-1 & 0 & -3\\
2 & 3 & 0
\end{bmatrix}[/tex] in ratio with the base:
[tex]E_1=\begin{bmatrix}
0 & 1 & 1\\
-1 & 0 & 0\\
-1 & 0 & 0
\end{bmatrix}[/tex]
[tex]E_2=\begin{bmatrix}
0 & 0 & 1\\
0 & 0 & 1\\
-1 & -1 & 0
\end{bmatrix}[/tex]
[tex]E_3=\begin{bmatrix}
0 & -1 & 0\\
1 & 0 & -1\\
0 & 1 & 0
\end{bmatrix}[/tex]
Homework Equations
antisymetric matrix is only if [itex]A^t=-A[/tex]
The Attempt at a Solution
The matrix is equal to:
[tex]f: \mathbb{R}^3 \rightarrow \mathbb{R}^3 , f(x_1,x_2,x_3)=(x_2-2x_3,-x_1-3x_3,2x_1+3x_2)[/tex]
The base is [tex]B={(x_2+x_3,-x_1,-x_1) ; (x_3,x_3,-x_1-x_2) ; (-x_2,x_1-x_3,x_2)}[/tex]
What should I do now?