Difference between revisions of "06-240/Classnotes For Tuesday October 3"
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'''Example.''' In <math>P_3(\mathbb{R})</math>, <math>v_1=2x^3-2x^2+12-6</math> is a linear combination of: <math>u_1=x^3-2x^2-5x-3</math> and <math>u_2=3x^3-5x^2-4x-9</math> but <math>v_2=3x^3-2x^2+7x+8</math> is not. | '''Example.''' In <math>P_3(\mathbb{R})</math>, <math>v_1=2x^3-2x^2+12-6</math> is a linear combination of: <math>u_1=x^3-2x^2-5x-3</math> and <math>u_2=3x^3-5x^2-4x-9</math> but <math>v_2=3x^3-2x^2+7x+8</math> is not. | ||
− | + | '''Why?''' <math>v_1=2x^3-2x^2+12-6=a_1u_1+a_2u_2</math> | |
− | + | <math>=a_1(x^3-2x^2-5x-3)+a_2(3x^3-5x^2-4x-9)</math> | |
− | <math>v_1 | + | |
− | + | ||
− | <math>=a_1(x^3-2x^2-5x-3)+a_2(3x^3-5x^2-4x-9) | + | |
<math>v_1^{}=-4u_1+2u_2</math> | <math>v_1^{}=-4u_1+2u_2</math> |
Latest revision as of 08:14, 12 July 2007
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Links to Classnotes
- PDF file by User:Alla: Week 4 Lecture 1 notes
- PDF file by User:Gokmen: Week 4 Lecture 1 notes
Definition. is a linear combination of elements in if and such that
Example. In , is a linear combination of: and but is not.
Why?