Why is the set {91 +124t² - 61t³, 66 − 58t +93t², 22 + 248t — 87t² } not a basis for P3(R)? Select all that apply. The set is linearly dependent. ✓ It is not a spanning set. The set contains too many elements. ✓ The set contains too few elements. It is not a subset of P3(R)
Why is the set {91 +124t² - 61t³, 66 − 58t +93t², 22 + 248t — 87t² } not a basis for P3(R)? Select all that apply. The set is linearly dependent. ✓ It is not a spanning set. The set contains too many elements. ✓ The set contains too few elements. It is not a subset of P3(R)
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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Transcribed Image Text:Why is the set
{ 91 + 124ť² – 61ť³, 66 − 58t + 93t², 22 + 248t − 87t² }
not a basis for P3(R)? Select all that apply.
The set is linearly dependent.
It is not a spanning set.
The set contains too many elements.
✓ The set contains too few elements.
It is not a subset of P3(R)
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Step 1: Define basis of a vector space and the condition for a non homogeneous system to be consistent
VIEWStep 2: Check whether the given set is linearly independent or not
VIEWStep 3: Check whether the given set is linearly independent or not
VIEWStep 4: Check whether the given set generates P3(R) or not
VIEWStep 5: Write the given system in matrix form
VIEWStep 6: Use elementary row operations
VIEWStep 7: Use the theorem in step 1
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