Linear Algebra: linear equations

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  • #1
Amy-Lee
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Show that if u and v are solutions of the linear system Ax = b, then w = 1/4 u + 3/4 v is also a solution of Ax = b.
 

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  • #2
Preno
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Just plug it in and use the fact that matrix multiplication is linear.
 
  • #3
Amy-Lee
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Plug what? where?

Ax=b, then b=uv ? and uv=w? uv = 1/4u + 3/4v?
 
  • #4
HallsofIvy
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You want to show that w "is also a solution of Ax= b".

So "plug" w in for x: Aw= what? Use the fact that w= (1/4)u+ (3/4)v and that A is a linear transformation.
 
  • #5
tiny-tim
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Show that if u and v are solutions of the linear system Ax = b, then w = 1/4 u + 3/4 v is also a solution of Ax = b.
Plug what? where?

Ax=b, then b=uv ? and uv=w? uv = 1/4u + 3/4v?

Amy-Lee, forget x …

you know that Au = b and Av = b,

so just carry on from there. :wink:
 
  • #6
Amy-Lee
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Amy-Lee, forget x …

you know that Au = b and Av = b,

so just carry on from there. :wink:

thanks TT, I will try that
 

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