1 1 -3 1. Let A = 1 1 -1 -4 (a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A), and Nul(A) respectively. Find the rank and nullity of A. Verify the rank theorem. (Hint: row(A) is the row space which is spanned by the rows of A). (b) Determine whether b = is in col(A), whether w = [ 2 2 4 -5| 7 is in row(A), and whether v = -1 is in null(A)?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
solve question 1 with complete explanation asap and get multiple upvotes
1
1 -3
1. Let A =
2
1
1
-1
-4
(a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A),
and Nul(A) respectively. Find the rank and nullity of A. Verify the
rank theorem. (Hint: row(A) is the row space which is spanned by the
rows of A).
1
(b) Determine whether b =
1
is in col(A), whether w =
[2 4 -5]
7
is in row(A), and whether v =
-1
is in null(A)?
2. Find the coordinate vector of ū =
(2, 3) relative to the basis B =
{(1,0), (1, 1)} in vector space R?.
3. Find the determinant by using elementary row reductions.
2
-2 -6 0
10 8
-1
8
3
-1
-2 3
Transcribed Image Text:1 1 -3 1. Let A = 2 1 1 -1 -4 (a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A), and Nul(A) respectively. Find the rank and nullity of A. Verify the rank theorem. (Hint: row(A) is the row space which is spanned by the rows of A). 1 (b) Determine whether b = 1 is in col(A), whether w = [2 4 -5] 7 is in row(A), and whether v = -1 is in null(A)? 2. Find the coordinate vector of ū = (2, 3) relative to the basis B = {(1,0), (1, 1)} in vector space R?. 3. Find the determinant by using elementary row reductions. 2 -2 -6 0 10 8 -1 8 3 -1 -2 3
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,