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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Row reduced matrix has coefficents

**Physics Forums | Science Articles, Homework Help, Discussion**