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Consider the linear transformation T: R^4 to R^3 defined by T(x, y, z, w) = (x...

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Advance Math

Consider the linear transformation T: R^4 to R^3 defined by T(x,y, z, w) = (x +2y +z, 2x +2y +3z +w, x +4y +2w)

a) Find the dimension and basis for Im T (the image of T)

b) Find the dimension and basis for Ker ( the Kernel of T)

c) Does the vector v= (2,3,5) belong to Im T? Justify theanswer.

d) Does the vector v= (12,-3,-6,0) belong to Ker? Justify theanswer.

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