Let U be a subspace of R", and let S = { ū, v, w } be a set of three non-zero vectors in R”.Fill in the blanks so that the following statements are true. If you believe you don't have enough informationto conclude anything for any of the cases, choose the answer "???".Note that there is no intended relationship between the parts. In each case, assume only what the statementsays to assume.If SCU, then dim(U) >(Enter the largest integer that makes the statement necessarily true.)If S is linearly independent and S C U, then dim(U) 3.If S' is a spanning set for U, then dim(U) 3.If span(S) = U then SIf S is a basis for U, then Slinearly independent.linearly independent. Suppose that is a vector of length 2 which is orthogonal to some other vector . Thenū · (2ū + 7v) + ||proj-(2ū) + projū||

If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and SC U, then dim(U) 3. If S is a spanning set for U, then dim(U) 3. If span(S) = U then S linearly independent. If S is a basis for U, then S linearly independent.

If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and SC U, then dim(U) 3. If S is a spanning set for U, then dim(U) 3. If span(S) = U then S linearly independent. If S is a basis for U, then S linearly independent.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 30E

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Question

Let U be a subspace of R", and let S = { ū, v, w } be a set of three non-zero vectors in R”.
Fill in the blanks so that the following statements are true. If you believe you don't have enough information
to conclude anything for any of the cases, choose the answer "???".
Note that there is no intended relationship between the parts. In each case, assume only what the statement
says to assume.
If SCU, then dim(U) >
(Enter the largest integer that makes the statement necessarily true.)
If S is linearly independent and S C U, then dim(U) 3.
If S' is a spanning set for U, then dim(U) 3.
If span(S) = U then S
If S is a basis for U, then S
linearly independent.
linearly independent.

Suppose that is a vector of length 2 which is orthogonal to some other vector . Then
ū · (2ū + 7v) + ||proj-(2ū) + projū||

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Step 1: Define linearly dependent set and spanning set property :-

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