Answered: Let P2 be the vector space of all… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 44EQ

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Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 9x - 8x2– 4, 7x – 10x2-7 and 2x - x2.
a The dimension of the subspace H is
b. Is (9x- 8x2 -4,7x– 10x²– 7,2x – x²) a basis for P2? choose
+ Be sure you can explain and justify your answer.
c. A basis for the subspace H is {
}. Enter a polynomial or a comma separated list of polynomials.

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Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 37. V = P, W is the set of all polynomials of degree 3
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
Find a basis for R3 that includes the vector (1,0,2) and (0,1,1).

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