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
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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![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)
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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)
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LARLINALG8 4.1.055.
MY NOTES](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f3dbc50-dc67-4eb1-b456-90badba3c3e7%2F88d0f94c-a48a-45b5-9fe1-67a2d565b67c%2F3tj1s5_processed.png&w=3840&q=75)
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
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[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: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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