This course will cover the following subjects:
Matrices: matrix operations, inverse of a matrix, solving systems of linear equations. Determinants: definition and properties, cofactor expansion and applications. Vectors in R2 and R3 , scalar and cross products, lines and planes, applications. The vector space Rn . subspaces, linear independence, basis and dimensions, orthogonality. Gram-Schmidt orthogonalization process. Rank of matrix. Eigenvalues and eigenvectors, diagonalization of a matrix.
Once a student pass this class, he/she will be able to:
✴Understand the role of matrices and vectors principles in various settings of life.
✴Apply the basic vectors and matrix operations in solving linear systems and matrix eigenproblems.
✴Apply some techniques in constructing and finding a basis for some subspaces and computing their dimensions.
✴Familiarize some matrix spaces (row space, column space, null space and eigenspace) and their dimensions (kernel and nullity) .
✴Compute the eigenpairs of a matrix and their relationship with the existence of the inverse of the matrix and linear independence of the eigenvectors.
