**Unformatted text preview: **1 x x 2 y-x y 2-x 2 z-x z 2-x 2 , det = ( y-x )( z 2-x 2 )-( z-x )( y 2-x 2 ) = ( y-x )( z-x )( z + x-y-x ) = ( y-x )( z-x )( z-y ) Singular for x = y or y = z or z = y Problem 4: Find the distance between the plane given by x-2 y + z = 0 and the point with coordinates p = (1 , , 0) SOLUTION: Basis for the subspace given by the plane: v = sb 1 + tb 2 , b 1 = 2 1 , b 2 = -1 1 , ( b T 1 b T 2 ) ( p-q ) = 0 , q = ( b 1 , b 2 ) ( s t ) B T B ( s t ) = B T p, s = 1 3 , t =-1 6 , q = . 8333 . 3333-. 1667 , p-q = . 1667-. 3333 . 1667 , d = | p-q | = 0 . 4082 2 This study resource was shared via CourseHero.com Powered by TCPDF ( )...

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