Show that the set B = {x² - -x+1, 3x² + 4, x - 2} is a basis of the (real) vector space of polynomials of degree ≤ 2. If p(x) = 1 + x + x², determine the coordinate vector [p(x)]B with respect to the given ordering.
Show that the set B = {x² - -x+1, 3x² + 4, x - 2} is a basis of the (real) vector space of polynomials of degree ≤ 2. If p(x) = 1 + x + x², determine the coordinate vector [p(x)]B with respect to the given ordering.
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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![Show that the set B = {x² -
-x+1, 3x² + 4, x - 2} is a basis of the (real) vector space of
polynomials of degree ≤ 2. If p(x) = 1 + x + x², determine the coordinate vector [p(x)]B with respect to
the given ordering.
Explain why the set
H = {(X1, X2, X3, X4) € Rª : x1 + x2 + x3 + x4 = 0}
is a subspace of R4. Decide whether the following vectors span H:
-0-0-0
V2 =
V1 =
3
-2
V3 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcde9fee-829a-403f-a1fa-44b86dc0b06a%2Fef93b504-5a26-4ff0-b492-cbe3a989cbbd%2Fttv91jj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that the set B = {x² -
-x+1, 3x² + 4, x - 2} is a basis of the (real) vector space of
polynomials of degree ≤ 2. If p(x) = 1 + x + x², determine the coordinate vector [p(x)]B with respect to
the given ordering.
Explain why the set
H = {(X1, X2, X3, X4) € Rª : x1 + x2 + x3 + x4 = 0}
is a subspace of R4. Decide whether the following vectors span H:
-0-0-0
V2 =
V1 =
3
-2
V3 =
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Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Write the given data
VIEWStep 2: Check the linear independece of the given set
VIEWStep 3: Check whether the given set spans the real vector space of polynomial of degree 2
VIEWStep 4: Check whether the given set spans the real vector space of polynomial of degree 2
VIEWStep 5: Determine the required cordinate vector
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