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## Tentative Schedule

Week of Contents Sections
1/26 Linear systems and their geometric interpretation. Matrices and vectors. The matrix form of a linear system. Gauss-Jordan elimination. 1.1-1.2
2/2 Matrix vocabulary. Operations on matrices. Space Rn. Rank of a matrix. Number of solutions of a linear system. 1.2-1.3
2/9-2/16 Linear transformations from Rm to Rn. Matrix of a linear transformation. Linear transformations in a plane: scalings, projections, reflections, rotations, shears. Composition of linear transformations and matrix product. Inverse linear transformation and invertible matrices. 2.1-2.4
2/23 Subspaces of Rn. Linear combinations of vectors. Span of vectors. Linear dependence and independence. Basis. Coordinates. Dimension. 3.1-3.4
3/2 Kernel and image of a linear transformation. Kernel- Image (Rank-Nullity) theorem.3.3
3/9 Midterm I on 3/9; Kernel- Image (Rank-Nullity) theorem. 3.3
3/16 Linear transformations and their matrices. Change of a basis. 3.4
3/22 Linear spaces. Linear transformations and their matrices. Isomorphisms. 4.1-4.2
3/30 Inner product spaces. Euclidean space Rn. Orthogonality. 5.1
4/6Spring break
4/13 Orthogonal projections. Orthogonal complement. Cauchy-Schwarz inequality, Pythagorean Theorem. Gram-Schmidt orthogonalization. General inner product spaces. 5.1 -5.2, some of 5.5
4/20 Midterm II on Apr 20; Determinants. 6.1
4/27 Determinants and their geometrical interpretation. Properties of determinants. 6.1-6.3
5/4 Eigenvalues and eigenvectors. Eigenspaces. Characteristic equation. Eigenbasis. Diagonalization. 7.1-7.4
Friday 5/15 11:00-1:30 Final exam