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(3) Assume in this part that S = Z3. Consider J := |x € Z3 -2x (a) Justify that J is the set of all non units of R (i.e., all the matrices in R having zero determinants in the field Z3). (b) Justify by finding a A E Z3 satisfying the condition in part (2)(ii) that J = I (implying that J is an ideal of R).

(3) Assume in this part that S = Z3. Consider J := |x € Z3 -2x (a) Justify that J is the set of all non units of R (i.e., all the matrices in R having zero determinants in the field Z3). (b) Justify by finding a A E Z3 satisfying the condition in part (2)(ii) that J = I (implying that J is an ideal of R).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(3) Assume in this part that S = Z3. Consider J :={ |x € Z3 -2x (a) Justify that J is the set of all non units of R (i.e., all the matrices in R having zero determinants in the field Z3). (b) Justify by finding a A E Zg satisfying the condition in part (2)(ii) that J = I (implying that J is an ideal of R).
Transcribed Image Text:(3) Assume in this part that S = Z3. Consider J :={ |x € Z3 -2x (a) Justify that J is the set of all non units of R (i.e., all the matrices in R having zero determinants in the field Z3). (b) Justify by finding a A E Zg satisfying the condition in part (2)(ii) that J = I (implying that J is an ideal of R).
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