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
A vector space is a mathematical structure that consists of a set of vectors and operations that can be performed on those vectors, such as addition and scalar multiplication. It is used in linear algebra to represent and manipulate quantities that have both magnitude and direction.
In order for a set of vectors to form a basis for a vector space, they must be linearly independent (meaning no vector in the set can be written as a linear combination of the others) and span the entire vector space (meaning any vector in the space can be written as a linear combination of the basis vectors).
A linear system of equations is a set of equations that can be written in the form of Ax=b, where A is a matrix, x is a vector of variables, and b is a vector of constants. The goal is to find a solution for x that satisfies all of the equations in the system.
Gaussian elimination is a method for solving a linear system of equations by using row operations to reduce the augmented matrix (a matrix that combines the coefficient matrix and the constants vector) into row-echelon form. This allows you to easily solve for the variables and find the solution to the system.
Eigenvalues and eigenvectors are important concepts in linear algebra. Eigenvalues are scalar values that represent how a linear transformation (represented by a matrix) affects the magnitude of a vector, while eigenvectors are the corresponding vectors that are only scaled by the transformation (but not rotated). They are useful for understanding the behavior of linear systems and are often used in applications such as data analysis and image processing.