MT210 MIDTERM 1 SAMPLE 2
ILKER S. YUCE
FEBRUARY 16, 2011
QUESTION 1. SYSTEMS OF LINEAR EQUATIONS
The augmented matrix of a linear system has the form
[a1 1
2a−1 1 ]
Determine the values of afor which the linear system is consistent.
1
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Augmented Matrix - Linear Algebra - Exam, Exams of Linear Algebra
These are the notes of Exam of Linear Algebra which includes Initial Value Problem, General Solution, Erential Equation, Origin Parallel, Line, Vector Space, Dimension etc. Key important points are: Augmented Matrix, Linear System, Values, Consistent, Corresponding, Reduction Algorithm, System is Consistent, General, Solution Set, Linear Combination
Typology: Exams
2012/2013
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MT210 MIDTERM 1 SAMPLE 2
ILKER S. YUCE
FEBRUARY 16, 2011
QUESTION 1. SYSTEMS OF LINEAR EQUATIONS
The augmented matrix of a linear system has the form
[ a 1 1 2 a − 1 1
]
Determine the values of a for which the linear system is consistent.
QUESTION 2. ROW REDUCTION AND ECHELON FORMS
Write the augmented matrix corresponding the system below:
x 1 − 6 x 2 − 4 x 3 = − 5 2 x 1 − 10 x 2 − 9 x 3 = − 4 −x 1 + 6 x 2 + 5 x 3 = 3_._
Solve the system by applying the row reduction algorithm. If the system is consistent, find the general solution set.
QUESTION 4. THE MATRIX EQUATION Ax=b
A.) Write the given matrix equation below as system of linear equations:
x 1 x 2 x 3
B.) Solve the system and write the general solution.
QUESTION 5. SOLUTION SETS OF LINEAR SYSTEMS
A. Solve the nonhomogeneous system Ax=b and write the solution in parametric vector form where
A =
(^) and b =
B. Using the parametric vector form of the solution set in part A., determine a particular solution p.
C. Write the general solution for the system A x = 0 in parametric vector form.