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Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (2x + 2y, x + y) B = 1 -1 2 1

Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (2x + 2y, x + y) B = 1 -1 2 1

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 93E
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Use a software program or a graphing utility with matrix capabilities to write v as a linear combination of u₁, U₂, U3, U4, and us. Then verify your solution. (Enter your answ U4, and u5.) V = v = U₁ = U₂ = (1, 2, 0, 2, 1) u3 = (0, 1, 1, 1, -4) U4=(2, 1, 1, 2, 1) us= (0, 2, 2, -1, -1) (5, 3, 8, 9, 11) (1, 2, 3, 4, -1) X Need Help? Read It [0/1 Points] 0 = DETAILS Need Help? X Watch It The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V2, and v3 because 0 = 0v₁ + Ov₂ + 0v3. This is called the trivial solution. Can you fir writing 0 as a linear combination of the three vectors? (Enter your answer in terms of V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.) V₁ = (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 7, 2) Read It PREVIOUS ANSWERS LARLINALG8 4.1.055. MY NOTES
Transcribed Image Text:Use a software program or a graphing utility with matrix capabilities to write v as a linear combination of u₁, U₂, U3, U4, and us. Then verify your solution. (Enter your answ U4, and u5.) V = v = U₁ = U₂ = (1, 2, 0, 2, 1) u3 = (0, 1, 1, 1, -4) U4=(2, 1, 1, 2, 1) us= (0, 2, 2, -1, -1) (5, 3, 8, 9, 11) (1, 2, 3, 4, -1) X Need Help? Read It [0/1 Points] 0 = DETAILS Need Help? X Watch It The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V2, and v3 because 0 = 0v₁ + Ov₂ + 0v3. This is called the trivial solution. Can you fir writing 0 as a linear combination of the three vectors? (Enter your answer in terms of V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.) V₁ = (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 7, 2) Read It PREVIOUS ANSWERS LARLINALG8 4.1.055. MY NOTES
Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (2x + 2y, x + y) B = 1 -1 2 1
Transcribed Image Text:Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (2x + 2y, x + y) B = 1 -1 2 1
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