Suppose A is a 3 x 4 matrix. (a) List all possible values for the rank of A (no justification necessary). (b) List all possible values for the nullity of A (no justification necessary). (c) Suppose you know that 2 3 A 6 and A 2 1 Do you have enough information to compute the product A -3 ? If so, compute it; if not, explain -2 clearly why not.
Suppose A is a 3 x 4 matrix. (a) List all possible values for the rank of A (no justification necessary). (b) List all possible values for the nullity of A (no justification necessary). (c) Suppose you know that 2 3 A 6 and A 2 1 Do you have enough information to compute the product A -3 ? If so, compute it; if not, explain -2 clearly why not.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Transcribed Image Text:Suppose A is a 3 x 4 matrix.
(a) List all possible values for the rank of A (no justification necessary).
(b) List all possible values for the nullity of A (no justification necessary).
(c) Suppose you know that
個-8
2
3
A
1
6.
and
A
1
3
1
Do you have enough information to compute the product A
-3
|? If so, compute it; if not, explain
-2
clearly why not.
Transcribed Image Text:Angwer
key
For part (a), the possible ranks (numbers of pivots) are 0, 1, 2, and 3. For part (b), the possible nullities
(numbers of non-pivot columns) are 1, 2, 3, and 4 (since A has four columns but only three rows, at least
one column must be a non-pivot column). For part (c), since
1
2
-3
-1
-2
1
1
and multiplication by A is linear, you do have enough information to compute
1
-3
A
-2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
