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)?
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
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78226682-8735-4a60-aea6-691d1e1816db%2F3496a1c4-584d-49dc-80f4-31aa0459bdfe%2Fn9zcgt9_processed.png&w=3840&q=75)
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
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