Non Row Reduced - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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Math 205A Quiz 01, page 1 September 14, 2007 = NAME Suggested Solshons 1 —2 -6 1 —2 3 9 _ |-3 1. Suppose u, = 5 [U2 = |_yg]> 4s = |_39 ,and uy = 3 4 —8 —24 2 1A. What is the (initial, non-row reduced) augmented matrix which corresponds to the system 15 of equations you need to solve in order to find out if the vector b = i in the span of the 50 vectors Uy, Us, Uz, and u4? = Le ‘ BO SERe ee ie ‘ 2 Ks @ 5h past é G Wb 49 2 LL Re ‘ ‘ 4 -§ 24 iz 50 ¢ NeoTE | We wall abd write Be : fa ana auynentack rnnkrix (te Look cee. rut) 1B. An augmented matrix which is row equivalent to the correct answer to (1A) is given below; you do not need to verify this. Use it to determine if b is indeed in the span of uj, we, Ug, and uy. If b is not in the span, explain why not. If it is in the span, find all the linear combinations of uy, Uy, U3, and uy which add up to b (that is, find the solution of the system of equations refered to in (1A); if there are any solutions write them in terms of the free variables (if there are any)). 100 0] 2 : _, | 0 1 3 0}-4 Row equivalent matrix: 0001] § 0000] 0 The aug meted matix Sroule po inconsislney @ tet Oe in the span f diy thy hy 5 FA solhen gf he syslon rere! ho x=2 The price of df X22 -Y-3x, yaenkl meas Be GO - ma xo He 2 OF tie oe a. Lis te oypes Bimal fds yy Xy =