Math Problem Statement

  1. 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

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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