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b-cl-lina.2011t

# b-cl-lina.2011t - Linear Algebra MAS4105 6137 Prof JLF King...

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Linear Algebra MAS4105 6137 Class-B Prof. JLF King 1Oct2011 B1: OYOP: Essay: Write on every third line, so that I can easily write between the lines. In grammatical English sentences , prove the following: Intersection thm. Suppose X and Y are subspaces of VS V . Prove that W := X Y is a subspace. [ Hint: First give a formal definition of what it means for a subset of V to be a sub space . ] B2: Show no work. Please write DNE in a blank if the described object does not exist or if the indicated operation cannot be performed. a With C the change-of-basis matrix from E := (1 , x, x 2 ) to B := (3 x + 5 x 2 , x + 2 x 2 , 1), then C 1 equals , C = . b Over Q , the inverse of E := 1 A C 1 B 1 is . c Glued to a massless plate is a 15 lb weight at the origin, a 5 lb weight at the point (3 , 1), and 10 lb at point ( . . . . . . . . . . . . , . . . . . . . . . . . . ) , thus putting the center-of-mass of the weighted-plate at (1 , 2). d Let M := 1 5 - 1 - 20 - 32 0 2 5 - 1 33 0 1 3 0 21 . Working over field Z 7 , matrix RREF ( M ) equals e Let R θ be the std. rotation [ by θ ] matrix. With C := 3 1 1 3 and B := 2 2 2 2 , the product [ CB ] 35 = α ·
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