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Problem 1: Find the matrix R³ = V W = R³ which sends the 2 basis {v₁ = ()--(0) (9). = , V3 = (9) ₁ C }CV to the basis {w₁ feel confident about your plan, try it for v₁ = = (-²2), ¹/2 = (1) ₁² Problem 2: Try to come up with a plan for how I might send a set of vectors {v₁, v₂} CV = R² to a set of vectors {w₁, W2} CR³ (Note the dimensions go from 2 to 3!). Once you (9) 1 2 , W₁ = (9) --- ().-.- ,W2 = W3 = - (1) ₁ C 0 and w₂ 2 () -1 2

Problem 1: Find the matrix R³ = V W = R³ which sends the 2 basis {v₁ = ()--(0) (9). = , V3 = (9) ₁ C }CV to the basis {w₁ feel confident about your plan, try it for v₁ = = (-²2), ¹/2 = (1) ₁² Problem 2: Try to come up with a plan for how I might send a set of vectors {v₁, v₂} CV = R² to a set of vectors {w₁, W2} CR³ (Note the dimensions go from 2 to 3!). Once you (9) 1 2 , W₁ = (9) --- ().-.- ,W2 = W3 = - (1) ₁ C 0 and w₂ 2 () -1 2

Advanced Engineering Mathematics
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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Problem 1: Find the matrix R³ = V W = R³ which sends the 2 basis {v₁ = ()--(0) (9). = , V3 = (9) ₁ C }CV to the basis {w₁ feel confident about your plan, try it for v₁ = = (-²2), ¹/2 = (1) ₁² Problem 2: Try to come up with a plan for how I might send a set of vectors {v₁, v₂} CV = R² to a set of vectors {w₁, W2} CR³ (Note the dimensions go from 2 to 3!). Once you (9) 1 2 , W₁ = (9) --- ().-.- ,W2 = W3 = - (1) ₁ C 0 and w₂ 2 () -1 2
Transcribed Image Text:Problem 1: Find the matrix R³ = V W = R³ which sends the 2 basis {v₁ = ()--(0) (9). = , V3 = (9) ₁ C }CV to the basis {w₁ feel confident about your plan, try it for v₁ = = (-²2), ¹/2 = (1) ₁² Problem 2: Try to come up with a plan for how I might send a set of vectors {v₁, v₂} CV = R² to a set of vectors {w₁, W2} CR³ (Note the dimensions go from 2 to 3!). Once you (9) 1 2 , W₁ = (9) --- ().-.- ,W2 = W3 = - (1) ₁ C 0 and w₂ 2 () -1 2
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