Linear Equation - Linear Algebra - Exam, Exams of Linear Algebra

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MT210 MIDTERM 1

İLKER S. YÜCE

FEBRUARY 20, 2011

SURNAME, NAME:

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 − 1 2 1 a − 1 3 1 1 b 3 − 5 5 1 c 2 − 2 4 2 d

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.