# MAT-291 Objectives

## MAT-291 Linear Algebra

### Chapter 1

1. Recognize a linear equation in n variables.
2. Find a parametric solution set for a linear equation.
3. Graph a system of linear equations.
4. Determine consistency for a system of linear equations.
5. Determine the size of a matrix.
6. Solve linear equations by the Gaussian method.
7. Solve equations by the Gauss-Jordan method.
8. Solve a homogeneous system of linear equation.
9. Solve a system of equations representing a network.
10. Translate a matrix into a system of linear equations.

### Chapter 2

1. Perform matrix operations.
2. Find the transpose of a matrix.
3. Find the inverse of a matrix.
4. Find the inverse of a matrix product.
5. Factor a given matrix.
6. Solve matrix equations.
7. Use stochastic matrices to measure consumer preference.
8. Use matrix multiplication to code and decode messages.
9. Use matrix algebra to analyze economic systems.
10. Find the factorization of a matrix.

### Chapter 3

1. Find the determinant of a given matrix.
2. Find the minors and cofactors of a determinant.
3. Expand cofactors to find determinant of a matrix.
4. Find the determinant of a triangular matrix.
5. Recognize zero determinants.
6. Use the properties of determinants.
7. Find the determinant of an elementary matrix.
8. Use determinants to decide singularity of matrices.
9. Verify eigenvalues and eigenvectors of a matrix.
10. Use the adjoint of a matrix to find its inverse.

### Chapter 4

1. Perform vector operations.
2. Determine whether a two operation set is a vector space.
3. Recognize vector spaces.
4. Determine whether a vector space subset is a subspace.
5. Recognize subspaces R2 and R3.
6. Write a vector as a linear combination.
7. Determine whether a set of vectors is a spanning set.
8. Find the dimension of a subspace.
9. Find the rank of a matrix.
10. Test sets of solutions for linear independence.

### Chapter 5

1. Find all orthogonal vectors to a given vector.
2. Determine whether two vectors are orthogonal, parallel, or neither.
3. Determine the inner product of two vectors.
4. Find the projection of a vector onto another vector.
5. Apply the Gram-Schmidt orthonormalization process.
6. Determine whether two subspaces are orthogonal.
7. Find the coordinates of an orthonormal basis in Rn.
8. Find the orthogonal compliment of a subspace.
9. Find unit vector in the same, or opposite, direction as v.
10. Verify the Cauchy-Schwarz Inequality, the Triangular Inequality and the Pythagorean Theorem for u and v.