(a) U = R3[x]. (b) U={A R3×3 | A diagonal }

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let V be the vector space of real upper triangular 2×2 matrices. To which of the listed spaces U is the space V isomorphic? The correct answer is (b). Why?

(a) U = R3[x].
(b) U={A R3×3 | A diagonal }<R3×3.
(c) U= {(x, y, z, w) ER4 | x+y=0, w+z = 0} <R4.
(d) U={p R₂[x] | p(1) = 0} < R₂[2].
(e) U L{} <R2×2.
Transcribed Image Text:(a) U = R3[x]. (b) U={A R3×3 | A diagonal }<R3×3. (c) U= {(x, y, z, w) ER4 | x+y=0, w+z = 0} <R4. (d) U={p R₂[x] | p(1) = 0} < R₂[2]. (e) U L{} <R2×2.
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