Preparation problems for the discussion sections on September 9th and 11th1. Determine if the vector−511−7is a linear combination of1−22,055,208.2. Give a geometric description of Span{302,−203}.3. True or false? Justify your answers!(a) Let A be an m × n-matrix and B be an m × l-matrix. Then the productAB is defined.(b) The weights c1, ..., cpin a linear combination c1v1+ ... + cpvpcannot allbe zero.(c) Span{u, v} contains the line through u and the origin.(d) Asking whether the linear system corresponding toa1a2a3b isconsistent, is the same as asking whether b is a linear combination ofa1, a2, a3.4. Determine whether2−16is a linear combination of the columns of1 0 5−2 1 −60 2 8.5. Compute AB in two ways: a) by the definition, where Ab1and Ab2arecalculated separately, and b) by the row-column rule for computing AB.i) A =4 −2−3 03 5, B =1 32 −1ii) A=5 1 06 0 1, B =6 10 −10 16. Let A =2 14 2.(1) If x =00, what is Ax?(2) If x =1−2, what is Ax?(3) Is Ax = b uniquely solvable: is there for a given b always exactly one x?17. (Some interesting matrices) Find a matrix A (what size!) such that• Axy=xy• Axy=xy + 3x.•
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