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Unformatted text preview: Practice Problems (1) Determine if the vector (2,0,3), can be expressed as a linear combi nation of the vectors (1,3,0) and (2,4,1). Solution: ( 2 , 3 , 0) = 4(1 , 3 , 0) + ( 3)(2 , 4 , 1) . (2) Determine if the polynomial 2 x 3 2 x 2 + 12 x 6 can be expressed as a linear combination of x 3 2 x 2 5 x 3 and 3 x 3 5 x 2 4 x 9 . Solution: 2 x 3 2 x 2 + 12 x 6 = ( 4)( x 3 2 x 2 5 x 3) + 2(3 x 3 5 x 2 4 x 9) . (of course, you have to ”find” a solution of a suitable system of equations to come up with this answer! (3) Determine if the polynomial 3 x 3 2 x 2 + 7 x + 8 can be expressed as a linear combination of x 3 2 x 2 5 x 3 and 3 x 3 5 x 2 4 x 9 . Solution: Start with 3 x 3 5 x 2 4 x 9 = a ( x 3 2 x 2 5 x 3) + b (3 x 3 5 x 2 4 x 9) and try to find a s olution of the system of equations. Show that there are no such a and b . (4) Determine if the matrix 1 2 3 4 is in the span of S = { A = 1 1 4 ,B = 0 1 0 1 ,C = 1 1 0 0 } ....
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 '08
 VATSAL
 Math, Linear Algebra, Vectors, Vector Space, Linear combination

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