Daftar Isi:1. Linear Equations and Matrices a. Systems of Linear Equations b. Matrices Matrix Operations c. Algebraic Properties of Matrix Operations d. Special Types of Matrices and Partitioned Matrices e. Echelon From a Matrix f. Elementary Matrices g. Equivalent Matrices h. LU-Factorization (Optional) 2. Real Vector Spaces a. Vectors in the Plane and in 3-Space b. Vector Spaces and Subspaces c. Linear Independence d. Basis and Dimension e. Coordinates and Isomorphisms f. The Rank of a Matrix 3. Inner Product Spaces a. The Standard Inner Product on R2 and R3 b. Cross Product in R3 (Optional) c. Inner Product Spaces d. The Gram Schmidt Process e. Least Squares (Optional) 4. Linear Transformations and Matrices a. Definition and Examples b. The Kernel and Range of a Linear Transformation c. The Matrix of a Linear Transformation d. The Vector Space of a Matrices and the Vector Space of Linear Transformations (Optional) e. Similarity 5. Determinants a. Definition b. Properties of Determinants c. Cofactor Expansion d. The Inverse of a Matrix e. Other Applications of a Determinants f. Determinants From a Computational Point of View 6. Eigenvalues and Eigenvectors a. Diagonalization b. Diagonalization of Symmetric Matrices c. Real Quadratic Forms d. Conic Sections e. Quadric Surfaces 7. Differential Equation