Which of the following sets are closed under scalar multiplication? (1) The set of all vectors in R of the form (a, b, 9ab). (11) The set of all polynomials a+ bx + cx in P, such that ac = 0. (iii) The set of all matrices in M, such that A- %3D

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Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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3: Which of the following sets are closed under scalar multiplication?
(1) The set of all vectors in R of the form (a, b, 9ab).
(i1) The set of all polynomials a- bx+ cx in P, such that ac =D0.
(iii) The set of all matrices in Mn such that A = A
(A) (1) and (ii) only (B) (1) and (iii) only (C) (ii) and (iii) only (D) (1) only (E) (ii) only (F) none of them
(G) (iii) only (H) all of them
Transcribed Image Text:3: Which of the following sets are closed under scalar multiplication? (1) The set of all vectors in R of the form (a, b, 9ab). (i1) The set of all polynomials a- bx+ cx in P, such that ac =D0. (iii) The set of all matrices in Mn such that A = A (A) (1) and (ii) only (B) (1) and (iii) only (C) (ii) and (iii) only (D) (1) only (E) (ii) only (F) none of them (G) (iii) only (H) all of them
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