Linear Algebra: linear equations

[Amy-Lee]

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.

 

[Preno]

Just plug it in and use the fact that matrix multiplication is linear.

 

[Amy-Lee]

Plug what? where?

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

 

[HallsofIvy]

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.

 

[tiny-tim]

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.

 

[Amy-Lee]

Amy-Lee, forget x …

you know that Au = b and Av = b,

so just carry on from there.

thanks TT, I will try that