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I want to determine to matrices, S and T, so that for the matrix B,

[tex]B=\left(\begin{array}{cccc}-1&-2&-5&-3\\1&1&4&2\\4&-3&9&1\\2&-6&0&-4\end{array}\right)[/tex]

it´s true that:

[tex]SBT=\left(\begin{array}{cc}E_k&0\\0&0\end{array}\right)[/tex]

where E_k is the identity matrix of dimension k x k and k is the rank of B

I successfully calculated that rg(B)=2 and I also have the vectors that solve Bx=0:

[tex]v_1=\left(\begin{array}{c}-3\\-1\\1\\0\end{array}\right)[/tex]

and

[tex]v_1=\left(\begin{array}{c}-1\\-1\\0\\1\end{array}\right)[/tex]

I don´t know why, but I cannot express the columns of B as linear combination of v_1 and v_2. I checked my calculations twice...?

I´m pretty sure it´s a basis change problem, but instead of having the two basis I have the transformed matrix.

How is one supposed to do such transformations?

Any help will be much appreciated!

Thanks a lot in advance!!!

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# Basis change matrix

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