-1 1 -2 4 8 -1 Consider the following matrix A = -2 -3 13 2 -1 4 -1 -11 3 16 1. Find a basis for Row(A). 1 2. Find a basis for Col(A). 8 13 3. Write the column as a linear combination of the basis vectors se- -11 16 lected in 2).
-1 1 -2 4 8 -1 Consider the following matrix A = -2 -3 13 2 -1 4 -1 -11 3 16 1. Find a basis for Row(A). 1 2. Find a basis for Col(A). 8 13 3. Write the column as a linear combination of the basis vectors se- -11 16 lected in 2).
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
![-1
1
-2
4
8
-1
Consider the following matrix A =|
2
-2
-3
13
2
-1
4
-1
-11
3
5
16
1. Find a basis for Row(A).
1
2. Find a basis for Col(A).
8
13
3. Write the column
as a linear combination of the basis vectors se-
-11
16
lected in 2).
4. Find a basis for Null(A).
-5
5. Find the value of k such that the vector b =
3
is in Null(A).
1
6. What is the rank of A and the nullity of A?
-2
000
8
-2
7. Is the set of vectors {
4
13
linearly dependent or indepen-
-1
-11
6.
16
dent? Justify.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce24d946-66cc-4b2e-8956-a056991a086b%2F0f54904f-6c58-4e28-8caf-dc66166df33e%2F39upkdw_processed.png&w=3840&q=75)
Transcribed Image Text:-1
1
-2
4
8
-1
Consider the following matrix A =|
2
-2
-3
13
2
-1
4
-1
-11
3
5
16
1. Find a basis for Row(A).
1
2. Find a basis for Col(A).
8
13
3. Write the column
as a linear combination of the basis vectors se-
-11
16
lected in 2).
4. Find a basis for Null(A).
-5
5. Find the value of k such that the vector b =
3
is in Null(A).
1
6. What is the rank of A and the nullity of A?
-2
000
8
-2
7. Is the set of vectors {
4
13
linearly dependent or indepen-
-1
-11
6.
16
dent? Justify.
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