LA06Homework3

LA06Homework3 - Practice Problems (1) Determine if the...

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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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LA06Homework3 - Practice Problems (1) Determine if the...

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