7) (Second Isomorphism Theorem): Let W C X be subspaces of V. Then V/X and (V/W)/(X/W) are isomorphic. Hint: Define T:V → (V/X) by T(u) = u+ X = [u]x, look at the transformation T : (V/W) (V/X) definted by î ([u]w) = T(u) = [u]x and apply the first isomorphism theorem.

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A: Here we can use the composition of function formula to find the required values.

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A: The kernel is a line with slope -1 and passes through the origin.

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A: The objective of the question is evaluate the zero element and inverse element.

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A: I am solving the first part for you.The given linear transformation is : from To find all vectors…

Q: '

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A: