201 Phys

1) Systems of linear equations and matrices: Introduction to systems of

linear equations, Gaussian elimination, Homogeneous Systems of linear

equations, Matrices and matrix operations, Rules of matrix arithmetic,

Elementary matrices and a method for finding inverse A.

2) Determinants: The determinant function, Evaluating determinants by row

reduction, Properties of the determinant function, Cofactor expansion,

Cramer's rule.

3) Vectors 2d-space and 3d-space: Introduction to vectors (Geometric),

Norm of a vector; vector arithmetic, Dot product; projections, Cross

product.

4) Vector spaces: Euclidean n-space, General vector spaces, Subspaces,

Linear independence, Basis and dimension, Row and column space of a

matrix; rank; Application to finding bases, Inner product spaces; length

and angle in inner product spaces, Orthonormal basis; Gram-Schmidt

process, Coordinates; change of basis.

5) Linear transformations: Introduction to linear transformations,

Properties of linear transformation: Kernel and Range.

6) Eigenvalues and eigenvectors: Eigenvalues and eigenvectors,

Diagonalization, Orthogonal Diagonalization.

Text Book:
Howard Anton, Elementary Linear Algebra, 11th edition, John Wiley & Sons, Inc.