Math 205b Quiz 01 Worksheet - 2010 printable pdf download

Math 205b Quiz 01 Worksheet - 2010

Quiz 01 page 1

01/15/2010

Math 205B

Name

4 100

1. Consider the augmented matrix A =

1A. What system of linear equations is represented by A?

1B. Find the reduced row echelon form (rref) of A by hand, showing all the matrices produced along the way. Say what

each elementary row operation was used to produce each new matrix from the previous one using the “r

← r

+ 4r

” style

notation we developed in class)

1C. What is the solution of the system in part 1A?





1 3

3 11 11

2. Consider the system of equations whose augmented matrix is B =

3 2

5 12

 .



5 1

13 13 11

Use your calculator to ﬁnd rref(B) and write the result in the space below. Circle the pivot columns of B. Then use the

rref to ﬁnd all the solutions of the system using the methods and notation we’ve developed in class. If there are no solutions,

explain why. Otherwise, give a speciﬁc solution and show it satisﬁes the ﬁrst equation the augmented matrix represents.





1 3

3 1 11

3 2

5 2

3. Now consider the system of equations whose augmented matrix is C =

 .



5 1

13 1 11

Again, use your calculator to ﬁnd rref(C) and write the result in the space below. Circle the pivot columns of C. Finally,

use the rref to ﬁnd all the solutions of the system using the methods and notation we’ve developed in class. If there are

no solutions, explain why; otherwise, give a speciﬁc solution and show it satisﬁes the ﬁrst equation the augmented matrix

represents.

Math 205b Quiz 01 Worksheet - 2010