linear algebra
This assignment covers the following measurable student objectives:
- Determine where a given matrix is singular.
- Find the inverse of a nonsingular matrix by applying to the identity matrix an appropriate set of row operations.
- Given that inverse of the coefficient matrix of a system of linear equations exists, use the inverse to solve the linear system.
- (worth 10 points) A system of linear equations only has three possibilities of a solution set. a. What are those three possibilities?
b. Cite the theorem from section 1.6 that states this fact. - (worth 10 points) What does it mean for a matrix to be singular? a. Give an example of a 2×2 matrix that is singular. b. Show why the matrix in 2a) is singular.
3. (worth 10 points) What does it mean for a matrix to be nonsingular?
- Give an example of a 3×3 matrix that is nonsingular.
- Show why the matrix in 3a) is nonsingular using the inversion algorithm.
4. (worth 20 points) Solve the system of linear equations below by inverting the coefficient matrix and using Theorem that states: If A is an invertible n x n matrix, then for each
n x 1 matrix b, the system of equations Ax = b has exactly one solution, namely, x = A-1b. Once you find the solution x, check that the solution x solves the system.
x1 + 3x2 + x3 = 4
2x1 +2x2 +x3 =–1
2x1 +3x2 +x3 =3
