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 $R^6$

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Asked by 3 years ago
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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. ### Your Answer Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0\$ or $$\beta^2-1=0$$

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Views: 45
Asked: 3 years ago