MAT-291 Objectives
MAT-291 Linear Algebra
Chapter 1
- Recognize a linear equation in n variables.
- Find a parametric solution set for a linear equation.
- Graph a system of linear equations.
- Determine consistency for a system of linear equations.
- Determine the size of a matrix.
- Solve linear equations by the Gaussian method.
- Solve equations by the Gauss-Jordan method.
- Solve a homogeneous system of linear equation.
- Solve a system of equations representing a network.
- Translate a matrix into a system of linear equations.
Chapter 2
- Perform matrix operations.
- Find the transpose of a matrix.
- Find the inverse of a matrix.
- Find the inverse of a matrix product.
- Factor a given matrix.
- Solve matrix equations.
- Use stochastic matrices to measure consumer preference.
- Use matrix multiplication to code and decode messages.
- Use matrix algebra to analyze economic systems.
- Find the factorization of a matrix.
Chapter 3
- Find the determinant of a given matrix.
- Find the minors and cofactors of a determinant.
- Expand cofactors to find determinant of a matrix.
- Find the determinant of a triangular matrix.
- Recognize zero determinants.
- Use the properties of determinants.
- Find the determinant of an elementary matrix.
- Use determinants to decide singularity of matrices.
- Verify eigenvalues and eigenvectors of a matrix.
- Use the adjoint of a matrix to find its inverse.
Chapter 4
- Perform vector operations.
- Determine whether a two operation set is a vector space.
- Recognize vector spaces.
- Determine whether a vector space subset is a subspace.
- Recognize subspaces R2 and R3.
- Write a vector as a linear combination.
- Determine whether a set of vectors is a spanning set.
- Find the dimension of a subspace.
- Find the rank of a matrix.
- Test sets of solutions for linear independence.
Chapter 5
- Find all orthogonal vectors to a given vector.
- Determine whether two vectors are orthogonal, parallel, or neither.
- Determine the inner product of two vectors.
- Find the projection of a vector onto another vector.
- Apply the Gram-Schmidt orthonormalization process.
- Determine whether two subspaces are orthogonal.
- Find the coordinates of an orthonormal basis in Rn.
- Find the orthogonal compliment of a subspace.
- Find unit vector in the same, or opposite, direction as v.
- Verify the Cauchy-Schwarz Inequality, the Triangular Inequality and the Pythagorean Theorem for u and v.