1. Write TRUE if the statement is always correct. Otherwise, write FALSE. 1. The set S = {(2, 8, 5), (0, 2, 7), (0, 0, 7)) is a basis for R³. 3. The set W = ((X₁, 8, X3): X₁ and x3 are real numbers) is a subspace of R³ with the s 3. The following subset of C(-∞, ) is a subspace of C(-∞, *). The set of all nonnegative functions: f(x) ≥ 0 4. The set S= {(1, 1, 1), (4, 4, 4), (9, 9, 9)} is linearly independent. 5. The following subset of C(-∞, ∞) is a subspace of C(-∞, ∞). 6. The set of all n x n lower triangular matrices is a subspace of Mn.n. The set of all constant functions: f(x) = c 7. The set S = ((-3, 2), (4, 5)} is linearly independent. 8. The set S= ((7, 1), (-1, 7)} spans R2². 9. The set S= (1, x², x2 + 2) spans P2. 10. The set S= {(-3, 3)} spans R
1. Write TRUE if the statement is always correct. Otherwise, write FALSE. 1. The set S = {(2, 8, 5), (0, 2, 7), (0, 0, 7)) is a basis for R³. 3. The set W = ((X₁, 8, X3): X₁ and x3 are real numbers) is a subspace of R³ with the s 3. The following subset of C(-∞, ) is a subspace of C(-∞, *). The set of all nonnegative functions: f(x) ≥ 0 4. The set S= {(1, 1, 1), (4, 4, 4), (9, 9, 9)} is linearly independent. 5. The following subset of C(-∞, ∞) is a subspace of C(-∞, ∞). 6. The set of all n x n lower triangular matrices is a subspace of Mn.n. The set of all constant functions: f(x) = c 7. The set S = ((-3, 2), (4, 5)} is linearly independent. 8. The set S= ((7, 1), (-1, 7)} spans R2². 9. The set S= (1, x², x2 + 2) spans P2. 10. The set S= {(-3, 3)} spans R
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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DUE NOW. Please answer all this true or false questions. No need for explanation, Just the correct answers. Thank you!
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1. Write TRUE if the statement is always correct. Otherwise, write FALSE.
1. The set S = {(2, 8, 5), (0, 2, 7), (0, 0, 7)} is a basis for R³.
2. The set W= {(x1, 8, X3): X₁ and x3 are real numbers) is a subspace of R³ with the s
3. The following subset of C(-∞, ) is a subspace of C(-∞, ∞).
The set of all nonnegative functions: f(x) ≥ 0
4. The set S= {(1, 1, 1), (4, 4, 4), (9, 9, 9)} is linearly independent.
5. The following subset of C(-∞, ∞) is a subspace of C(-∞, ∞).
6. The set of all n x n lower triangular matrices is a subspace of Mn.n-
The set of all constant functions: f(x) = c
7. The set S = {(-3, 2), (4, 5)} is linearly independent.
8. The set S= ((7, 1), (-1, 7)} spans R².
9. The set S= (1, x², x + 2) spans P2.
10. The set S= {(-3, 3)} spans R².
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