Constraint Equations: Get the Answers You Need

[jhg12345]

Thanks so much guys

 

[Mark44]

Homework Statement

Find constraint equations that b must satisfy in order to be an element of
b. V= Span ((1,0,1,1),(0,1,1,2),(1,1,1,0)

Homework Equations

None

The Attempt at a Solution

I get the matrix
[1 0 0 -2
0 1 0 -1
0 0 1 3]. What's the restraint equation?

Let's rename b to x, since I want to use a, b, c, and d as the coordinates of this vector.
In this problem you want to find solutions for c₁, c₂, and c₃ so that c₁<1, 0, 1, 1> + c₂<0, 1, 1, 2> + c₃<1, 1, 1, 0> = <a, b, c, d>.

Is that enough to get you started?

 

[jhg12345]

Yea, that's what I did and I got a matrix, but I can't get a matrix with a row of all zeros.

 

[Mark44]

Use an augmented 4 x 4 matrix with your three vectors as the first three columns, and the coordinates a, b, c, and d as the fourth column.

From the matrix you showed, it looks like you have your three vectors as rows in a 3 x 4 matrix.

 

[jhg12345]

ok thanks for the help so far, but I am still stuck.

 

[Mark44]

Use the third row to eliminate the 2 entry in the row above it. Then, use the 4th row to eliminate any nonzero entries above it.

Where is your 4th column? You need that to get your constraint equation.

 

[jhg12345]

Yea, I know. Thanks for the help.