Solving a Linear Combination Problem

[guyvsdcsniper]

Homework Statement

Determine whether b can be written as a linear combination of and . In other words, determine whether weights x1 and x2 exist, such that . Determine the weights and if possible

Relevant Equations

x1a1+x2a2=b

I have attached my work to this thread.

Could someone help me with this Linear Algebra problem. This is my first week so I do not know many advanced ways to solve these problems.

I could not figure out how to get this matrix into rref, so I solved it the following way. Is the way I used appropriate? Is it possible to get this in rref? I am breaking my head trying to think of how I can get it to that form.

 

[FactChecker]

I'm not sure what other method you are trying to use for a solution. What you did is a very standard way of solving that problem. I agree with your work.

 

[Steve4Physics]

Homework Statement:: Determine whether b can be written as a linear combination of and . In other words, determine whether weights x1 and x2 exist, such that . Determine the weights and if possible
Relevant Equations:: x1a1+x2a2=b

I have attached my work to this thread.

Could someone help me with this Linear Algebra problem. This is my first week so I do not know many advanced ways to solve these problems.

I could not figure out how to get this matrix into rref, so I solved it the following way. Is the way I used appropriate? Is it possible to get this in rref? I am breaking my head trying to think of how I can get it to that form.

If you want a method in terms of row operations, mayabe this video will help (about 10 mins):