Linear Algebra and Score Student Number

~61E

LINEAR ALGEBRA

QUESTION ı

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22 MAY 2013

FINAL

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[ı2 pts] (a) Find the transition matrix from the ordered basis [(ı, ı, ı)T, (ı, 0, O)T, (0,2, ı)T] of R3 to the ordered basis [(2,ı, O)T, (0, ı, O)T, (ı, 2, ı)T] of R3.

[13 pts] (b) Let A

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2

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.

5

(i) Find a basis for the row space of A and determine its dimension.
(ii) Find a basis for the column space of A and determine its dimension.
(iii) Find the rank of A.

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