If $C$ is $6 \times 6$ and the equation $Cx =v$ is consistent for every $v$ in $R^6$

If $C$ is $6 \times 6$ and the equation $Cx =v$ is consistent for every $v$ in $R^6$


A
Asked by 3 years ago
45 points

If $C$ is $6 \times 6$ and the equation $Cx =v$ is consistent for every $v$ in $R^6$, is it possible that for some $v$, the equation $Cx=v$ has more than one solution? Why or why not?

If $C
Adrian

1 Answer

Answered by 3 years ago
8.7k points

Since $Cx=v$ is consistent for every $v$ in $\Bbb R^6$ then by the invertible matrix theorem $C$ is invertible which implies that that each equation $Cx=v$ has a unique solution.

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Views: 45
Asked: 3 years ago

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