2) Let X be a finite dimensional vector space and S, T are subsets of X such that SST then a) If S basis for X then T basis for X. b) If T generate X then S generate X. c) If T basis for X then S basis for X. d) If S generate X then T generate X. 3) Let Z, be ring integers mode 5 and f(x) € Z5 (x) such that f(x) = x² + 2x + 1 then a) f(x) has only one root. b) f(x) has only two roots. c) f(x) irreducible polynomials. d) No one of above. 4) Let R be a ring and F-M₂(R) be ring of 2 x 2 matrices over R under standard addition and multiplication of matrices then: a) F is a commutative ring but not field. b) F is a division ring and not field. c) If F an integral domain and F is not field. d) No one of above.
2) Let X be a finite dimensional vector space and S, T are subsets of X such that SST then a) If S basis for X then T basis for X. b) If T generate X then S generate X. c) If T basis for X then S basis for X. d) If S generate X then T generate X. 3) Let Z, be ring integers mode 5 and f(x) € Z5 (x) such that f(x) = x² + 2x + 1 then a) f(x) has only one root. b) f(x) has only two roots. c) f(x) irreducible polynomials. d) No one of above. 4) Let R be a ring and F-M₂(R) be ring of 2 x 2 matrices over R under standard addition and multiplication of matrices then: a) F is a commutative ring but not field. b) F is a division ring and not field. c) If F an integral domain and F is not field. d) No one of above.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:2) Let X be a finite dimensional vector space and S, T are subsets of X such that S ST
then
a) If S basis for X then T basis for X.
b) If T generate X then S generate X.
c) If T basis for X then S basis for X.
d) If S generate X then T generate X.
3) Let Z3 be ring integers mode 5 and f(x) € Zg(x) such that f(x) = x²
a) f(x) has only one root.
b) f(x) has only two roots.
c) f(x) irreducible polynomials..
d) No one of above.
+ 1 then
4) Let R be a ring and F-M₂(R) be ring of 2 x 2 matrices over R under standard
addition and multiplication of matrices then:
a) F is a commutative ring but not field.
b) F is a division ring and not field.
c) If F an integral domain and F is not field.
d) No one of above.
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