30. In the vector space R2x2, 1 A = 0. 1 0 B = C = -1 -3 1 are given. (a) Is {A, B, C} linearly independent? (b) Use the standard inner product in R2x2 to find an orthogonal basis for the subspace W =< A, B,C>. 1. (c) Which matrix in (A, B,C) is closest to
30. In the vector space R2x2, 1 A = 0. 1 0 B = C = -1 -3 1 are given. (a) Is {A, B, C} linearly independent? (b) Use the standard inner product in R2x2 to find an orthogonal basis for the subspace W =< A, B,C>. 1. (c) Which matrix in (A, B,C) is closest to
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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Please solve the question of a,b and c options.
![30. In the vector space R²×²,
1
A =
0.
[: :]. c-[]
1 0
1 0
В
-3 1
-
are given.
(a) Is {A, B, C} linearly independent?
(b) Use the standard inner product in R²×2 to find an orthogonal basis
for the subspace W =< A, B,C >.
1
(c) Which matrix in (A, B,C) is closest to
-1 1
0 2 2
2 0 2
2 0
31. Let A](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea935b3f-096e-44be-b5ef-dc725a70e21a%2F5a8816e0-93f1-4b6a-a749-2e7f60b93a4a%2Fwr0v2co_processed.jpeg&w=3840&q=75)
Transcribed Image Text:30. In the vector space R²×²,
1
A =
0.
[: :]. c-[]
1 0
1 0
В
-3 1
-
are given.
(a) Is {A, B, C} linearly independent?
(b) Use the standard inner product in R²×2 to find an orthogonal basis
for the subspace W =< A, B,C >.
1
(c) Which matrix in (A, B,C) is closest to
-1 1
0 2 2
2 0 2
2 0
31. Let A
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