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IGED 120-02 Spring 2018 Foundations Quantitative Reasoning
Assignment in lieu of class lecture on February 22, 2018. SHOW ALL OF YOUR WORK (attach
additional sheets if necessary)
You may work in groups of no more than four persons. You can hand in one assignment per
group. Ensure that all group member names are on the assignment.
This is due at the beginning of class on Tuesday, February 27, 2018.
This assignment covers the following measurable student objectives:
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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.
1. (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.
2. (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.
1
Dr. Kim Barnette
MA 225 Spring 2018
3. (worth 10 points) What does it mean for a matrix to be nonsingular?
a. Give an example of a 3×3 matrix that is nonsingular.
b. 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 + 3×2 + x3 = 4
2×1 + 2×2 + x3 = –1
2×1 + 3×2 + x3 = 3
2
Dr. Kim Barnette
MA 225 Spring 2018
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