Linear Algebra Solutions 29

# Linear Algebra Solutions 29 - are linearly dependent for...

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are linearly dependent for precisely those values of λ for which the equation xX 1 + yX 2 + zX 3 = 0 has a non–trivial solution. This equation is equivalent to the system of homogeneous equations λx - y - z = 0 - x + λy - z = 0 - x - y + λz = 0 . Now the coeFcient determinant of this system is f f f f f f λ - 1 - 1 - 1 λ - 1 - 1 - 1 λ f f f f f f = ( λ + 1) 2 ( λ - 2) . So the values of λ which make X 1 , X 2 , X 3 linearly independent are those λ satisfying λ 6 = - 1 and λ 6 = 2. 5. Let A be the following matrix of rationals: A = 1 1 2 0 1 2 2 5 0 3 0 0 0 1 3 8 11 19 0 11 . Then A has reduced row–echelon form B = 1 0 0 0 -
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## This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.

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