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Find (a) ker(T), (b) nullity(T), (c) range(T), and (d) rank(T). A = [ 4/ 9 4/ 9 2/ 9 ] [ -4/9 4/9 -2/9 ]

Find (a) ker(T), (b) nullity(T), (c) range(T), and (d) rank(T).

A = [ 4/ 9 4/ 9 2/ 9 ]

[ -4/9 4/9 -2/9 ]

[ 2/9 -2/9 1/9 ]

Hi i need help with this matrix, i'm specially having trouble getting the range(T), NOT the basis of the range, i have the answer but i don't know how did get it, i'm looking for a detail explanation on how we find the range ,appreciate your help.

Larson, Ron. Elementary Linear Algebra (Page 318). Brooks Cole. Kindle Edition.

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