Linear Algebra Sample Midterm Exam Questions, Exams of Linear Algebra

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MT210 MIDTERM 1 SAMPLE 1

ILKER S. YUCE

FEBRUARY 16, 2011

QUESTION 1. SYSTEMS OF LINEAR EQUATIONS

Determine the values of k such that the linear system

9 x 1 + kx 2 = 9 kx 1 + x 2 = − 3 is consistent.

QUESTION 2. ROW REDUCTION AND ECHELON FORMS

Determine when the augmented matrix below represents a consistent linear system.  

1 0 2 a 2 1 5 b 1 − 1 1 c

QUESTION 4. THE MATRIX EQUATION Ax=b

A. Solve the matrix equation A x = b where

A =

 (^) , b =

B. Is it possible to solve A x = b for any given b =

b 1 b 2 b 3

 (^) where A is the matrix given in part A? Explain.

C. Describe the set of all b =

b 1 b 2 b 3

 (^) for which A x = b does have a solution.

QUESTION 5. SOLUTION SETS OF LINEAR SYSTEMS

Consider the linear system A x = b where

A =

 (^) , b =

A. Solve the linear system. B. Write the general solution in parametric-vector form. C. Give a particular solution p. D. Write the solution set for the homogeneous equation A x = 0.