The discussion centers on Problem 14 from the Linear Algebra Wikibook, specifically regarding the vectors (3,1,2)T and (2,0,2)T. These vectors indeed define the same plane as the vectors <3, 1, 2> and <0, -1, 1>. To verify this, one can compute the cross product of the vector pairs, which will yield normals to the respective planes, confirming their equivalence. Additionally, the question about reducing the matrix without transposing it was raised, indicating a need for clarity on matrix operations.
PREREQUISITESStudents of linear algebra, educators teaching vector spaces, and anyone seeking to deepen their understanding of linear systems and vector operations.
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.Nope said: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?
Nope said:also, can I reduce the matrix without transpose?
thanks
Homework Equations
The Attempt at a Solution