Please show detailed answer steps ( Linear algebra) b) V(F) = R³(R), W (F) = R?(R) two vector spaces and L:R3 → R?, L(x, y, z) = (2x +y + 2z,x +y +z) Let there be a linear transformation defined by....

Please show detailed answer steps ( Linear algebra)

Extracted text: Please show detailed answer steps ( Linear algebra) b) V(F) = R³(R), W (F) = R?(R) two vector spaces and L:R3 → R?, L(x, y, z) = (2x +y + 2z,x +y +z) Let there be a linear transformation defined by. Defining the Ker L and Im L subspaces dim(Ker L) + dim(Im L) = dim(R³) Verify the equation. Some of Im L R? extend to a base of.