Graduate Engineering - Linear Algebra (Graham Schmidt + more)

[Koolaidbrah]

Homework Statement

No idea how to solve this using graham schmidt. I know how to do graham schmidt and how to solve this problem if I didn't have to use graham schmidt, but I have no idea where to start in order to get my vectors to add to V

Found c to be 87 by using vector addition/subtraction and making it linearly dependent on other two.
However, not sure how to find two vectors that are in span and perpendicular that add up to V just like in #1

For b., as long as A is invertable, wouldn't it be all of the b vectors?

Homework Equations

Graham Schmidt...

The Attempt at a Solution

Posted above

 

[STEMucator]

Well, if the question was not asking you to use the procedure, you could easily solve the augmented system and exhibit a solution.

The point of the gram process though, is to take a set of linearly independent vectors say S, in your space and to form a orthogonal set of vectors T by using the process. The span of the new set of vectors will be equivalent to the span of your original set.

That is, span{T} = span{S}.

You could go even further and form an orthonormal set out of the vectors of T, but it's not required here. Finding the set T should be sufficient.

 

[Koolaidbrah]

Well, if the question was not asking you to use the procedure, you could easily solve the augmented system and exhibit a solution.

The point of the gram process though, is to take a set of linearly independent vectors say S, in your space and to form a orthogonal set of vectors T by using the process. The span of the new set of vectors will be equivalent to the span of your original set.

That is, span{T} = span{S}.

You could go even further and form an orthonormal set out of the vectors of T, but it's not required here. Finding the set T should be sufficient.

Should I use my first two vectors in my set to find the first orthogonal vectors and the third as {1 2 3} to find the vector V2 perpindicular to my span? From there {1 2 3} minus the V2 vector to get my V1

I'm just confused as to how I use V1 is in span, V2 is perp to span and V1+V2 = {1 2 3}

 

[member 392791]

Out of curiosity (I'm learning gram schmidt for the first time in my LA class), what application does this have to engineering? (Thinking of going into engineering)

 

[vela]

Should I use my first two vectors in my set to find the first orthogonal vectors and the third as {1 2 3} to find the vector V2 perpindicular to my span? From there {1 2 3} minus the V2 vector to get my V1

I'm just confused as to how I use V1 is in span, V2 is perp to span and V1+V2 = {1 2 3}

Yeah, that'll work if you're planning to do what I think you're saying.