Math Problem Statement
- For each set of vectors in R 3 given below, describe geometrically the set of all linear combinations ( line, plane or all of R 3 ). (a) {(1, −1, 1),(1, 2, 0),(4, 5, 1)} (b) {(1, 2, −3),(−2, −4, 6),(−3, −6, 9)} (c) {(2, −1, 0),(−1, 2, −1),(0, −1, 2)}
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear algebra
Vectors
Span
Formulas
Determinant calculation for 3x3 matrices
Theorems
Linear dependence and independence in vector spaces
Suitable Grade Level
Advanced undergraduate level
Related Recommendation
Geometric Description of Linear Combinations in R^3 Vectors
Solution Set of a System of Linear Equations in R3: Line, Plane, Point, or Empty Set?
Linear Algebra Homework: Vectors, Basis, and Subspaces
Determining Linear Dependence of Vectors in R^3: Example Solution
Linear Map T: R^2 to R^3 Example Problem Solution