m43q4f07soln - x =-2-3 t. In the second equation the...

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MATH 43 Solutions to 4th Quiz September 19, 2007 NAME: (Last, First) 2. Find the system of equations with the aumented matrix 1 0 3 - 2 0 1 - 2 1 . (New instructions: Do solve the system!) This matrix is a “reduced row echelon” matrix. We’re supposed to be able to solve by “just write out the equations,” with no computation. The system is x + 3 z = - 2 y - 2 z = 1 . We identify z as the free variable (as will be explained) and use z = t as our parameter. We solve the first equation for the leading variable, which is x in this case, and get
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Unformatted text preview: x =-2-3 t. In the second equation the leading variable is y, and we get y = 1 + 2 t. We recognize these as parametric equations of a line, with vector form [ x, y, z ] = [-2 , 1 , 0] + t [-3 , 2 , 1] , which is our solution of this linear system. 2 1. For the system 2 x 1 + 2 x 2-3 x 4 = 0-x 1-x 2 + x 3 + x 4-x 5 = 2 x 1 + x 2 + x 3-2 x 4-x 5 = 2 the augmented matrix is 2 2-3-1-1 1 1-1 2 1 1 1-2-1 2 . Solution:...
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This note was uploaded on 02/29/2008 for the course MATH 43 taught by Professor Dodson during the Spring '08 term at Lehigh University .

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m43q4f07soln - x =-2-3 t. In the second equation the...

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