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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![**Why is the set \(\{91 + 124t^2 - 61t^3, 66 - 58t + 93t^2, 22 + 248t - 87t^2\}\) not a basis for \(P_3(\mathbb{R})\)? Select all that apply:**
- [ ] The set is linearly dependent.
- [x] It is not a spanning set.
- [ ] The set contains too many elements.
- [x] The set contains too few elements.
- [ ] It is not a subset of \(P_3(\mathbb{R})\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82714d6b-e6ea-4543-ad11-70ca51290dd2%2F9fb63aa4-7085-45c2-bb61-de6b583298a3%2Fawd54g_processed.png&w=3840&q=75)
Transcribed Image Text:**Why is the set \(\{91 + 124t^2 - 61t^3, 66 - 58t + 93t^2, 22 + 248t - 87t^2\}\) not a basis for \(P_3(\mathbb{R})\)? Select all that apply:**
- [ ] The set is linearly dependent.
- [x] It is not a spanning set.
- [ ] The set contains too many elements.
- [x] The set contains too few elements.
- [ ] It is not a subset of \(P_3(\mathbb{R})\).
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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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