Question: Given the linear transformation defined by T ( x , y , z , t ) = ( x + 2 y + z +

Given the linear transformation defined byT(x,y,z,t)=(x+2y+z+t,2x+4y+3z,x+2yz+5t) it is asked:

a) Determine a basis for the nucleus of T.

b) Determine a basis for the image of T.

c) Determine whether T is one-to-one and/or surjective and justify.

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