MATH 1553 Quiz: MATH 1553 GT Quiz 2 1 1 1 2 Solutionsm1553
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Math 1553 quiz 2: 1. 1 and 1. 2 (10 points, 10 minutes) If a system of 4 linear equations in 3 variables is consistent, it must have a unique solution. Justify your answer: (3 pts) write an augmented matrix in reduced row echelon form corresponding to a consistent system of three linear equations in the variables x1, x2, x3, in which x2 is the only free variable. Such a consistent system can have fewer than 3 pivot columns, and thus a free variable. For example, the following augmented matrix represents a system of 4 equations in 3 variables which has in nitely many solutions. 0 0 0 0: the rst and third columns below (corr. to x1 and x3) are the pivot columns. The system is consistent and x2 is free. 2. (5 points) solve the following system of equations by putting an augmented matrix in reduced row echelon form.
