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Problem 3. Let 21, 22, 23, 41, 42, y3 be some real numbers, and let A= (1 12 13 (41 42 43); Prove (slowly) that dim (ker(A))

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A . dim (ker(A)) 2 (9 Jm(cCA))1 dim Crs (A)) A inan map A com be identficd A: R3 By rank- Nullity thorem, Nudity LA) 3. dim (

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