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Fundamental subspace theorem

Consider the matrix

a=(1 1 2
1 2 -1
3 2 1
5 5 2)

Find N(A), R(A), N(A^T),R(A^T). Show that the fundamental subspace theorem holds: N(A^T)=R(A)^(upside down T), N(A)=R(A^T)^(upsidedown T).

Hint: Notice that the fourth row is the sum of the first three rows.

Solution Summary

This gives a matrix and then proves that the fundamental subspace theorem holds.

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