I just want to confirm these two questions. Thanks in advance.(adsbygoogle = window.adsbygoogle || []).push({});

(1) Describe all solutions of Ax=0in parametric vector form, where A is row equivalent to the given matrix.

[tex]\left(\begin{array}{uvwxyz}1 & 5 & 2 & -6 & 9 & 0 \\0 & 0 & 1 & -7 & 4 & -8\\0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0\end{array}\right)[/tex]

There are no solutions because row 3 and 4 contradict eachother. Row 3 implies no solution.

(2) Suppose A is a 3x3 matrix andyis a vector in R^{3} such that the equation Ax=ydoes not have a solution. Does there exist a vectorzin R^{3} such that the equation Ax = z has a unique solution?

I said no because if the vectorydoes not have a solution in R^{3}, then this implies the last row of the row reduced matrix has coefficents that are all zero. Therefore, it either has no solution or an infinite number of solutions.

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# Row reduced matrix has coefficents

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