Quiz 8 Blank

Quiz 8 – Take Home (5 pts) This quiz is due in class on Thursday, April 16 . For credit you must show work for #1; otherwise you need only provide a correct answer. Late quizzes will not be accepted. th

Name__________________________________________ Class Time __________ Class no. _________ 1. (1) Convert the I.V.P., conditions. Show your work.

; y(0) = 1, y (0) = 0, y (0) = 2, y (0) = 0 into a corresponding system and initial The system

2. (2) Find the matrix products Ax(t) and A (t) to determine if x(t) = (t) =

are solutions of

A =

Ax =

Initial Conditions

and

and

where A =

.

T or F is a solution of

.

T or F x is a solution of

.

3. (1) For the system shown, show the corresponding completely-reduced augmented matrix. Based on your reduced matrix, determine if the system has a unique solution, no solution, or infinitely-many solutions. Reduced augmented matrix

Check ( ) correct conclusion

___Unique solution ___No solution ___Infinitely-many solutions 4.

(1) Express the infinitely-many solutions of the system with reduced augmented matrix as a linear combination of vectors, e.g., scalars. x=

, where v1, v2, v3 are vectors and x1, x2, x3 are