Find all 2 x 2 matrices A for which E(sub 7) =R^2.

Does E(sub 7) mean there are 7 eigenspaces? Can someone clarify this problem further?

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- December 1st 2009, 01:18 PMnoles2188Eigenspaces and eigenvectors
Find all 2 x 2 matrices A for which E(sub 7) =

**R**^2.

Does E(sub 7) mean there are 7 eigenspaces? Can someone clarify this problem further? - December 1st 2009, 02:14 PMtonio
- December 1st 2009, 07:14 PMnoles2188
According to my book:

E(sub 7) = ker(A - 7I(sub 2)) = {**v**[IMG]file:///C:/Users/Geoffrey/AppData/Local/Temp/moz-screenshot.png[/IMG]in**R**^2 : A**v**= 7**v**}

7 is an eigenvalue and, to me, the question is asking to find matrices A such that A**v**= 7**v**. How would I go about this? - December 2nd 2009, 12:12 AMlepton
denotes the eigenspace associated with the eigenvalue 7.

- December 2nd 2009, 03:40 AMtonio