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Hi:

I have a problem about combine bases from subspaces. This is part of orthogonality.

The examples as following:

For A=##\begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix}## split x= ##\begin{bmatrix} 4 \\ 3 \end{bmatrix}## into ##x_r##+##x_n##=##\begin{bmatrix} 2 \\ 4 \end{bmatrix}+\begin{bmatrix} 2 \\ -1 \end{bmatrix}##

I don't know why it can split into ##x_r##+##x_n##, and how to prove that,

thanks a lot

I have a problem about combine bases from subspaces. This is part of orthogonality.

The examples as following:

For A=##\begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix}## split x= ##\begin{bmatrix} 4 \\ 3 \end{bmatrix}## into ##x_r##+##x_n##=##\begin{bmatrix} 2 \\ 4 \end{bmatrix}+\begin{bmatrix} 2 \\ -1 \end{bmatrix}##

I don't know why it can split into ##x_r##+##x_n##, and how to prove that,

thanks a lot

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