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GOAL Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace.
Which of the subsets of
5.
.
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Linear Algebra with Applications (2-Download)
- Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R3 whose components are Pythagorean triples.arrow_forwardSubsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R3 whose components are nonnegative.arrow_forwardSubsets That are Not Subspaces In Exercises 7-20, W is not a subspace of V. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R2 whose components are integers.arrow_forward
- Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R2 whose second component is the square of the first.arrow_forwardSubsets That are Not Subspaces In Exercises 7-20, W is not a subspace of V. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R2 whose first component is 2.arrow_forwardSubsets That are Not Subspaces In Exercises 7-20, W is not a subspace of V. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R3 whose third component is 1.arrow_forward
- Proof Prove that if S1 and S2 are orthogonal subspaces of Rn, then their intersection consists of only the zero vector.arrow_forwardSubsets That are Not Subspaces In Exercises 7-20, W is not a subspace of V. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R2 whose components are rational numbers.arrow_forwardCalculus Let W1,W2,W3,W4, and W5 be defined as in Example 5. Show that Wi is a subspace of Wj for ij. Example 5 Subspaces of Functions Calculus Let W5 be the vector space of all functions defined on [0,1], and let W1,W2,W3, and W4 be defined as shown below. W1=setofallpolynomialfunctionsthataredefinedon[0,1]W2=setofallfunctionsthataredifferentiableon[0,1]W3=setofallfunctionsthatarecontinuouson[0,1]W4=setofallfunctionsthatareintegrableon[0,1]ShowthatW1W2W3W4W5andthatWiisasubspaceofWjforij.arrow_forward
- Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all non-negative functions in C(,).arrow_forwardDetermine subspaces of Mn,n In Exercises 2936, determine whether the subsetMn,n is a subspace ofMn,nwith the standard operations. Justify your answer. The set of all nn diagonal matricesarrow_forwardLet 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_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning