math54 - quiz 1 - solns

# math54 - quiz 1 - solns - Math 54 Quiz 1 Solutions 1(2 pts...

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Math 54 Quiz 1 Solutions 1. (2 pts) Convert the system of equations x 1 + 2 x 2 + 2 x 4 + 3 x 5 = 1 x 3 + 3 x 4 + 2 x 5 = - 1 x 3 + 4 x 4 - x 5 = 1 x 5 = 0 to augmented matrix form. Is the matrix in (a) echelon form, (b) reduced echelon form, or (c) neither? The matrix form is 1 2 0 2 3 1 0 0 1 3 2 -1 0 0 1 4 -1 1 0 0 0 0 1 0 This is in (c) neither echelon nor in reduced echelon form, because of the 1 directly below a pivot in column 3. 2. (4 pts) Find the solution set of the system of equations from problem 1. We use the matrix form found in number 1 and put it in reduced echelon form. We subtract row 3 from row 4 to get the following matrix. 1 2 0 2 3 1 0 0 1 3 2 -1 0 0 0 1 -3 2 0 0 0 0 1 0 Next we use the fourth row to cancel everything in the fifth column, the result looks like 1 2 0 2 0 1 0 0 1 3 0 -1 0 0 0 1 0 2 0 0 0 0 1 0 1

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Finally we use the third row to cancel everything in the fourth column.
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