Consider the functionT:R3→R3defined byT(x,y,z) = (3x,x−y,2x+y+z).(i) Prove thatTis a linear transformation. (T’nin bir lineer d ̈on...

Consider the functionT:R3→R3defined byT(x,y,z) = (3x,x−y,2x+y+z).(i) Prove thatTis a linear transformation. (T’nin bir lineer d ̈on ̈u ̧s ̈um oldu ̆gunu g ̈osteriniz)(ii) Find the representing matrix ofTrelative to the basisβ={α1= (1,0,0),α2= (1,1,0),α3=(1,1,1)}ofR3.(R3 ̈unβ={α1= (1,0,0),α2= (1,1,0),α3= (1,1,1)}tabanına g ̈oreTnin matris g ̈osterimini bulunuz.)

Expert Solution

The solution is given below

milcah answered 2 years ago

solve by determinants a.x+y+z=0 3x-y+2z=-1 2x+3y+3z=-5 b. x+2z=1 2x-3y=3 y+z=1 c. x+y+z=10 3x-y=0 3y-2z=-3 d. -8x+5z=-19...

solve by determinants a.x+y+z=0 3x-y+2z=-1 2x+3y+3z=-5 b. x+2z=1 2x-3y=3 y+z=1 c. x+y+z=10 3x-y=0 3y-2z=-3 d. -8x+5z=-19 -7x+5y=4 -2y+3z=3 e. -x+2y+z-5=0 3x-y-z+7=0 -2x+4y+2z-10=0 f. 1/x+1/y+1/z=12 4/x-3/y=0 2/y-1/z=3

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