hw2 - Math 260, Spring 2012 Jerry L. Kazdan Problem Set 2...

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Unformatted text preview: Math 260, Spring 2012 Jerry L. Kazdan Problem Set 2 Due: In class Thursday, Jan. 26. Late papers will be accepted until 1:00 PM Friday . 1. Which of the following sets of vectors are bases for R 2 ? a). { (0 , 1) , (1 , 1) } b). { (1 , 0) , (0 , 1) , (1 , 1) } c). { (1 , 0) , (- 1 , } d). { (1 , 1) , (1 ,- 1) } e). { ((1 , 1) , (2 , 2) } f). { (1 , 2) } 2. a) Compute the dimension of the intersection of the following two planes in R 3 x + 2 y- z = 0 , 3 x- 3 y + z = 0 . b) A map L : R 3 R 2 is defined by the matrix L := parenleftbigg 1 1- 1 3- 3 1 parenrightbigg . Find the nullspace (kernel) of L . 3. For which real numbers x do the vectors: ( , 1 , 1 , 1), (1 ,, 1 , 1), (1 , 1 ,, 1), (1 , 1 , 1 , ) not form a basis of R 4 ? For each of the values of x that you find, what is the dimension of the subspace of R 4 that they span? 4. Compute the dimension and find bases for the following linear spaces....
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hw2 - Math 260, Spring 2012 Jerry L. Kazdan Problem Set 2...

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