Linear Algebra Solutions 87

# Linear Algebra Solutions 87 - x + y-2 z = 1 x + 3 y-z = 4 ....

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Alternatively , we can calculate the distance OP 2 , where P is an arbitrary point on the line AB and then minimize OP 2 : P = A + t - AB = - 2 1 3 + t 3 1 1 = - 2 + 3 t 1 + t 3 + t . Hence OP 2 = ( - 2 + 3 t ) 2 + (1 + t ) 2 + (3 + t ) 2 = 11 t 2 - 4 t + 14 = 11 µ t 2 - 4 11 t + 14 11 = 11 ˆ t - 2 11 ¾ 2 + 14 11 - 4 121 ! = 11 ˆ t - 2 11 ¾ 2 + 150 121 ! . Consequently OP 2 11 × 150 121 for all t ; moreover OP 2 = 11 × 150 121 when t = 2 / 11. 8. We Frst Fnd parametric equations for N by solving the equations
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Unformatted text preview: x + y-2 z = 1 x + 3 y-z = 4 . The augmented matrix is • 1 1-2 1 1 3-1 4 ‚ , which reduces to • 1-5 / 2-1 / 2 1 1 / 2 3 / 2 ‚ . Hence x =-1 2 + 5 2 z, y = 3 2-z 2 , with z arbitrary. Taking z = 0 gives a point A = (-1 2 , 3 2 , 0), while z = 1 gives a point B = (2 , 1 , 1). 90...
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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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