Unformatted text preview: dimension. Alternatively, you can do the following: see if you can generate 1 from these polynomials, then try to generate x and x 2 , etc. until it is obviously impossible ( x 3 is impossible here, for example). Then count how many you have generated. 3. Let E = { u 1 , u 2 } , F = { v 1 , v 2 } be two bases in R 2 . where u 1 = ± 1 2 ² , u 2 = ± 3 4 ² , v 1 = ± 4 3 ² , v 2 = ± 2 1 ² . If x = 5 u 1 + 6 u 2 , ﬁnd the coordinate of x in F . Verify your answer in the end. Most people did this right. If not, read the book. 4. Let x ∈ R m , y ∈ R n be nonzero vectors in R m and R n , respectively, and let A = xy T . What is the dimension of N ( A )? Explain. Try with some actual vectors x and y , see if you can read the row space and the column space. It is easy to see the rank is 1 and one can proceed to ﬁnd dimension of N ( A ) by a Theorem in the book....
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 Spring '10
 wuyiling
 Linear Algebra, Vector Space, nontrivial coeﬃcient vector, nonsingular matrix

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