PDF-Test1ReviewSolutionMath342(1)Determinewhetherf(x;y;z)2R3:x+y+z=1gisasu
Author : heavin | Published Date : 2021-01-05
2SolutionLetUbeasubspaceofafdvectorspaceVandspanv1v2111vnVUbeingasubspaceofViscontainedinspanv1v2111vnBasisisalwayssmallerthanaspanningsetinlengthdimU20nSoUis12
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Test1ReviewSolutionMath342(1)Determinewhetherf(x;y;z)2R3:x+y+z=1gisasu: Transcript
2SolutionLetUbeasubspaceofafdvectorspaceVandspanv1v2111vnVUbeingasubspaceofViscontainedinspanv1v2111vnBasisisalwayssmallerthanaspanningsetinlengthdimU20nSoUis12. NULLSPACEANDNULLITY2UsingjustA;weuserowopsto ndreducedrowechelonform:211001001 2042003111 2122002112 413?R3 4R1!R3R4 R1!R4R5 2R1!R5R6 R1!R62110010 200 1001 20001 2000000002 403?R4 R3!R4R6 2R3!R6211001 Figure1.StereographicprojectionTheformulaforstereographicprojectionis(x;y;z)=x+iy 1 z:Indeed,thepoint(1 t)n+t(x;y;z)haslastcoordinate1 t+tz.Thisequals0fort=1=(1 z),makingtheothercoordinatesx=(1 z)and
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