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**Unformatted text preview: **List of important topics for the final exam: Sections 4.1 and 4.2: Line, Plane, and Projections. Sections 1.1, 1.2, and 1.3 (Systems of linear equations):- Perform EROs to transform a matrix to an REF or RREF matrix.- Solve a system of linear equations using Gaussian Elimination Method, and Gauss-Jordan Method.- Conditions for a homogeneous system to have a non-trivial solution. Sections 2.1, 2.2, and 2.3 (Matrix algebra):- Addition, subtraction, scalar multiplication, transpose and multiplication of matrices- Express the solution of homogeneous systems in terms of combinations of vectors.- Matrix inverses and properties of inverse. Optional: In Section 2.2, Theorem 2 on Page 41 (about associated homogeneous system of a linear system) and Example 8 are optional. Sections 2.4, 2.5 and 4.4:- Elementary matrices.- Transformations in general.- Projections, reflection and rotation....

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