1-Suppose that S1and S2are nonzero subspaces, with S1 contained inside S2, and suppose that dim(S2)=3 (a) What are the possible dimensions of S1? (b) If S1≠S2then what are the possible dimensions of S1? 2-Find the dimensions of the following linear spaces. (a) ℝ4×2 (b) P3 (c) The space of all diagonal 6×6 3-Find a basis {p(x),q(x)} for the vector space {f(x)∈P2[x]∣f′(4)=f(1)}where P2[x] is the vector space of polynomials in xx with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5+3x^2 p(x) , q(x)= 4-A square matrix is half-magic if the sum of the numbers in each row and column is the same. Find a basis BB for the vector space of 2×2 half-magic squares. B=

1-Suppose that S1and S2are nonzero subspaces, with S1 contained inside S2, and suppose that dim(S2)=3 (a) What are the possible dimensions of S1? (b) If S1≠S2then what are the possible dimensions of S1? 2-Find the dimensions of the following linear spaces. (a) ℝ4×2 (b) P3 (c) The space of all diagonal 6×6 3-Find a basis {p(x),q(x)} for the vector space {f(x)∈P2[x]∣f′(4)=f(1)}where P2[x] is the vector space of polynomials in xx with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5+3x^2 p(x) , q(x)= 4-A square matrix is half-magic if the sum of the numbers in each row and column is the same. Find a basis BB for the vector space of 2×2 half-magic squares. B=

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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