Which of the following sets are closed under scalar multiplication? (i) The set of all matrices in M22 such that A2 = A (ii) The set of all vectors in R° of the form (a, b, 8a+ 6b). (iii) The set of all polynomials a + bx + cx² in P2 such that ac = 0.
Which of the following sets are closed under scalar multiplication? (i) The set of all matrices in M22 such that A2 = A (ii) The set of all vectors in R° of the form (a, b, 8a+ 6b). (iii) The set of all polynomials a + bx + cx² in P2 such that ac = 0.
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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Transcribed Image Text:Which of the following sets are closed under scalar multiplication?
(i) The set of all matrices in M2 such that A
= A
(ii) The set of all vectors in R° of the form (a, b, 8a + 6b).
(iii) The set of all polynomials a + bx + cx- in P2 such that ac =
0.
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