Solution Set - Linear Algebra - Solved Exam, Exams of Linear Algebra

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Math 205B Test 1 (60 points) Name: Solu kio ns e Check that you have 7 questions on two pages. ® Show all your work to receive full credit for a problem. 1. (10 points) (For this problem do all calculations by hand.) Determine all possible values of h and k such that the solution set of the following system {a) is empty (b} contains infinitely many solutions Qa, +hrg = 5 eee = L2= @2-28) Augmented mebix is 9: h Ee 4) 2 i, BP | 4 3 kJ |o 3-2) k-lo : wt 5 Ca) Solabion sek is emphy if 3-2,=0 ie h= FZ and fe be : bh & (ay tris case, ednced mobin looks bke [; ee a a pa he tb) 3-2h=o0 it h=% and k-l0o=0 fe k=O: (Ee ° atm Ta tuts case, ue have one fre vorieble and So in finstely mary SolAs- 2. (8 points) Let A= [@) @ dg dy] be a3 x 4 matrix. Suppose a) = 3,02 = 4,73 = 1,24 = 2 is a solution of the equation Aq = 0. (a) Are the coluinns of A linearly independent? Explain. Columns of A Gee not newly independen t became we equation Ax=O har a non bimiat Solubers a amely i (b) Write the vector @ as a linear combination of the vectors @,, @, and a. We haw 3a 444, + 4,¢ 24,= "0 S$ f8,= -34,-44, -4, &, = 3% - os =~ 34)-26, 45,