10. If the vector v = (2, 2, 1, 1, 0) is in the null space of Г1 -3 2 2 -21 4 -3 -10 1 A = 2 -3 -2 4 | 1 -4 2 3 for a, B E R, which of the following statements are correct? I. Rank(A) = 2. II. The dimension of the null space of A is 2. Ш. {(1, 4, 2, 1), (-3, —3, —3, 0), (-2, 1, 0, 3)} is a basis for the column space of A. IV. {(1, –3, 2, 2, –2),(0, 1, -2, 0, 1)} is a basis for the row space of A.
10. If the vector v = (2, 2, 1, 1, 0) is in the null space of Г1 -3 2 2 -21 4 -3 -10 1 A = 2 -3 -2 4 | 1 -4 2 3 for a, B E R, which of the following statements are correct? I. Rank(A) = 2. II. The dimension of the null space of A is 2. Ш. {(1, 4, 2, 1), (-3, —3, —3, 0), (-2, 1, 0, 3)} is a basis for the column space of A. IV. {(1, –3, 2, 2, –2),(0, 1, -2, 0, 1)} is a basis for the row space of 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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![10. If the vector v =
(2, 2, 1, 1, 0) is in the null space of
[1 -3
2 -2]
4
A =
2
-3
-10
1
-3
-2
4
[1 B
-4
2
3
for a, B E R, which of the following statements are
correct?
I. Rank(A)
2.
%3D
II. The dimension of the null space of A is 2.
III. {(1, 4, 2, 1),(-3, –3, –3, 0),(-2, 1, 0, 3)}
is a basis for the column space of A.
IV. {(1, –3, 2, 2, –2),(0, 1, -2, 0, 1)} is a basis
for the row space of A.
(a)
II only
(b)
II, III
(c)
I, IV
(d)
П, IV
(e)
II, III, IV](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc18d56e-0798-4761-9c3e-f6d493a2d8ff%2Ffcadc61e-c826-4e03-af4f-a8c62458f180%2Fqg1nygq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10. If the vector v =
(2, 2, 1, 1, 0) is in the null space of
[1 -3
2 -2]
4
A =
2
-3
-10
1
-3
-2
4
[1 B
-4
2
3
for a, B E R, which of the following statements are
correct?
I. Rank(A)
2.
%3D
II. The dimension of the null space of A is 2.
III. {(1, 4, 2, 1),(-3, –3, –3, 0),(-2, 1, 0, 3)}
is a basis for the column space of A.
IV. {(1, –3, 2, 2, –2),(0, 1, -2, 0, 1)} is a basis
for the row space of A.
(a)
II only
(b)
II, III
(c)
I, IV
(d)
П, IV
(e)
II, III, IV
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