Linear Algebra: Vector Spaces & Linear Systems Problem 14

[Nope]

Homework Statement

http://en.wikibooks.org/wiki/Linear_Algebra/Vector_Spaces_and_Linear_Systems/Solutions
Problem 14
Can answer be (3,1,2)^T (2,0,2)^T?
also, can I reduce the matrix without transpose?
thanks

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

http://en.wikibooks.org/wiki/Linear_Algebra/Vector_Spaces_and_Linear_Systems/Solutions
Problem 14
Can answer be (3,1,2)^T (2,0,2)^T?

Yes. These vectors determine the same plane as the vectors <3, 1, 2> and <0, -1, 1>. To check yourself, take the cross product of the two pairs of vectors. Each cross product gives you a normal to a plane that contains the two vectors.

You get different vectors, but each is a scalar multiple of the other, so each of the two planes is the same.

also, can I reduce the matrix without transpose?
thanks

Homework Equations

The Attempt at a Solution