Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 9 -7 A = 1 1 1 -1 (a) ker(T) -5,3, – 1 (b) nullity(T) (c) range(T) {(s, t, s - 8t): s, t are any real number} {(s, t, 0): s, t are any real number} {(8s, 8t, s - t): s, t are any real number} R3 R2 (d) rank(T)

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A: The solution is given by using rank nullity theorem and null space as follows :

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