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Show that vector vec(a)=(5,9,14) can be written as linear Combination of vector bे 2 vec(c){:[=>" let " vec(a)=(x","y","z)],[ vec(b)=(-2","3","1)],[ vec(c)=(3","1","4)]:}Let a^(-1) is linear Combination of b^(-1)& vec(c)(x,y,z)=alpha(-2,3,1)+beta(3,1,4)Solving{:[(x","y","z)=(-2alpha+3beta","2alpha+beta","alpha+4beta)],[=>-2alpha+3beta=x-oo],[3alpha+beta=y-2],[alpha+4beta=z]:}sobigg (1) & (8){:[=>quad-2alpha+3beta=x],[+(2alpha+8beta=2z)/(11 beta=x+2z)],[beta=(x+2z)/(11)]:}Similarly solvin ... See the full answer