Hi, can anyone help me with this question?
Let S be the subspace of R4 given by the solution set of the equations
x2 - 3 x3 = -x2 - x3 - x4 and x1 = x1 + x3 = x1 - 2 x4
Find An example of a matrix for which S is the nullspace
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Write each equation on the form where are scalars. A possible matrix will "appear".
for the second equation, doesn't the x1 just cancel out?
your equations are equivalent to:
we can model this system of equations with the matrix equation:
the fact that x1 "cancels out" is indeed relevant, it shows we are completely free to choose ANY value for it.
Are you sure those are the right equations? immediately gives . And immediately gives . So immediately, vectors in the solution space are of the form . And your other equation, becomes which is equivalent to or .
it seems perfectly conceivable that A (the matrix in question) could have a 1-dimensional nullspace.
Last edited by Deveno; March 16th 2012 at 11:02 AM.
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