Math 136Assignment 5Due: Wednesday, Feb 15th1.LetA=12-13-2-1,B=10002-3,C=5-121-12. Determine the following(a) 2A-B(b)A(BT+CT)(c)BAT+CAT2.Findt1, t2, t3∈Rsuch thatt11101+t22002+t302-11=63333.Determine which of the following mappings are linear. Find the standard matrix, a basisfor the kernel, and a basis for the range of each linear mapping.(a)f(x1, x2, x3) = (x1+x2+ 1, x3,0).(b)f(x1, x2) = (0, x1+ 2x2, x2).(c) proj~awhere~a=-214.Determine the standard matrix of a reflection inR2in the linex1-5x2= 0.5.LetLandMbe linear mappings fromRntoRm, and letk∈R.(a) Prove that
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