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[M] Show that w is in the subspace of ℝ4 spanned by v1, v2, v3, where
w =
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Chapter 4 Solutions
Linear Algebra and Its Applications (5th Edition)
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- In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}arrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,arrow_forwardConsider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less than or equal to k, with standard operations. Show that if jk, then Pj is the subspace of Pk.arrow_forward
- 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 3arrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}arrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba+b+1]}arrow_forward
- In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=M22,W={[abcd]:adbc}arrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=M22,W={[abb2a]}arrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1arrow_forward
- 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?arrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set of diagonal nn matricesarrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=F,W=finF:f(x)=f(x)arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning