Question

Solving Systems of Linear Equations Using Linear Transformations
In problems 2 and 5 find a basis for the solution set of the homogeneous linear systems.

2. ?1 + ?2 + ?3 = 0
?1 − ?2 − ?3 = 0

5. ?1 + 2?2 − 2?3 + ?4 = 0
?1 − 2?2 + 2?3 + ?4 = 0.

So I'm in a Linear Algebra class at the moment, and the professor wants us to work through our homework using methods only covered during/before this homework assignment.

Topics I have covered thus far:

- Vector Spaces

-Subspaces

-Linear Systems and Linear Combinations

-Linear independence

-Basis and Dimension

-Linear Transformations

-Matrix representation of a linear transformation

-Composition of Linear Transformations

-Isomorphisms

-Elementary Matrices

-A matrix's rank and calculating inverse matrices

-solving systems of linear equations using linear transformations

Answer 1