MATH 315 (091) ASSIGNMENT 2
Please hand in Monday Sept. 15 at the beginning of class.
1. Refer to Exercises 3(d) and 4(d) in Section 1.3, and carry out the following steps. Show your
work (including row operations.)
(a) Write down the system of equations that has the given matrix as its augmented matrix. Also,
write down the coefficient matrix for this system.
(b) Find the reduced echelon form (RREF) for the augmented matrix. Show all of your row opera-
tions.
(c) Identify the pivot columns. Which variables in your system are the pivot variables?
(d) Write down the solution set of the system in vector form, showing the translation vector and
the spanning vector(s).
2. Let [a b]tbe any vector in R2, and let sbe the set of two vectors
S=Ω∑ 1
−1∏,∑2
2∏æ.
(a) Write down a system of equations in the variables xand ythe solution of which implies that
[a b]tbelongs to the span of S.
(b) Prove that [a b]tbelongs to the span Sby solving the system.
3. Do True/False questions 1, 2, and 7 in Section 1.4
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