2. Find the coordinate vector of i = (2,3) relative to the basis B = {(1,0), (1, 1)} in vector space R². %3D
2. Find the coordinate vector of i = (2,3) relative to the basis B = {(1,0), (1, 1)} in vector space R². %3D
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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solve question 2 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). [9 marks]
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%2F856ea4ca-8155-4d2b-917c-25578d48e63a%2Fcfd9d559-eebd-4e15-b172-f61c17f66b10%2Fpngyzwb_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). [9 marks]
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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