Difference between revisions of "06240/Classnotes For Tuesday October 3"
From Drorbn
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'''Example.''' In <math>P_3(\mathbb{R})</math>, <math>v_1=2x^32x^2+126</math> is a linear combination of: <math>u_1=x^32x^25x3</math> and <math>u_2=3x^35x^24x9</math> but <math>v_2=3x^32x^2+7x+8</math> is not.  '''Example.''' In <math>P_3(\mathbb{R})</math>, <math>v_1=2x^32x^2+126</math> is a linear combination of: <math>u_1=x^32x^25x3</math> and <math>u_2=3x^35x^24x9</math> but <math>v_2=3x^32x^2+7x+8</math> is not.  
−  +  '''Why?''' <math>v_1=2x^32x^2+126=a_1u_1+a_2u_2</math>  
−  +  <math>=a_1(x^32x^25x3)+a_2(3x^35x^24x9)</math>  
−  <math>v_1  +  
−  +  
−  <math>=a_1(x^32x^25x3)+a_2(3x^35x^24x9)  +  
<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

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?