Let P be the vector space of all polynomials of degree at most 3 with real coefficients, and let H = {a + bt³|a and b are real.} Which of the following is/are true? A. {1, +³} is linearly independent in H. B. {1, +³} is a basis for H. 4 C. H is a subspace of P. O A and C only O A, B, and C O A and B only O A only B and C only

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let P be the vector space of all polynomials of degree at most 3 with real coefficients, and let
H = {a + bt³|a and b are real.} Which of the following is/are true?
A. {1, +³} is linearly independent in H.
B. {1, +³} is a basis for H.
4
C. H is a subspace of P.
O A and C only
O A, B, and C
O A and B only
O A only
B and C only
Transcribed Image Text:Let P be the vector space of all polynomials of degree at most 3 with real coefficients, and let H = {a + bt³|a and b are real.} Which of the following is/are true? A. {1, +³} is linearly independent in H. B. {1, +³} is a basis for H. 4 C. H is a subspace of P. O A and C only O A, B, and C O A and B only O A only B and C only
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