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Matrices problem

  • Thread starter Derill03
  • Start date
  • #1
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x1[0,0,0] + x2[1,1,0] + x3[0,1,0] + x4[-1,-1,0] + x5[0,0,1] + x6[1,0,-1] = [4,0,2]

** left to right is top to bottom **


I am first asked to find 3 columns that span R3, I found that [-1,-1,0],[0,0,1],[1,0,-1] span r3 because they have a non-zero determinant. Now the next question is where i have trouble

I am asked to express the right side as a linear combination of the three columns i chose?

How can i write the three columns as a linear combination? I havent been able to find any really good explanation of a linear combination, can ne one help?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
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It just means, find three numbers a, b, c such that
a [-1, -1, 0] + b [0, 0, 1] + c [1, 0, -1] = [4, 0, 2]

The left hand side is called a linear combination of [-1, -1, 0], [0, 0, 1] and [1, 0, -1].
 
  • #3
63
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ok then if i've done this correctly it should be:

0*[-1,-1,0] + 6*[0,0,1] + 4*[1,0,-1] = [4,0,2]

a=0
b=6
c=4
 

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