
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
The solutions to quiz 01 of math 205b, focusing on finding the reduced row echelon form (rref) of augmented matrices and solving systems of linear equations using elementary row operations. Students are required to find the rref of three matrices (a, b, and c) and use the results to find the solutions of the corresponding systems.
Typology: Exercises
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Math 205B (^) Quiz 01 page 1 01/15/
1A. What system of linear equations is represented by A?
lB. Find the reduced row echelon form (rref) of A by hand, showing all the matrires produced along the way. Say what each elementary row operation was used to produce each new matrix from the previous one using the "rs +- r3 + 4r2" style notation we developed in class)
/
'OO
J
I -2.
I
I
1C. What is the solution of the system in part 1A?
~~)j 1 13 13 11 ~
/
O
J
1
W
11
: 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. H there are no solutions, explain why; otherwise, give a specific solution and show it satisfies the first equation the augmented matrix represents.
1
tJMsPtc,ihl.sJJW;.. l1k /11vIfckJr It in fk tI~VMl;o X I +-J X1.-1~ J + ~'1 = II : f 7 7 /' 2 i-3(f4) -1{o) ~(-J)--==II ~ 2+/2-3 ":'/1 # 1/=-111/