38. Let A be the matrix given in Exercise 26. a) For each vector b that follows, determine whether b is in R(A). b) If b is in R(A), then exhibit a vector x in R² such that Ax = b. c) If b is in R(A), then write b as a linear combination of the columns of A. [2] [1] 6 - [8] [3] -3 i) b = -[0] iii) b = 3 [2] -6 v) b = ii) b = iv) b = vi) b =
38. Let A be the matrix given in Exercise 26. a) For each vector b that follows, determine whether b is in R(A). b) If b is in R(A), then exhibit a vector x in R² such that Ax = b. c) If b is in R(A), then write b as a linear combination of the columns of A. [2] [1] 6 - [8] [3] -3 i) b = -[0] iii) b = 3 [2] -6 v) b = ii) b = iv) b = vi) b =
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
![In Exercises 26-37, give an algebraic specification for
the null space and the range of the given matrix A.
1-2
3
-3
6
2-6
[]
[12]
26. A =
28. A =
30. A =
32. A =
34. A =
36. A =
37. A =
1-1
2-1
13
27
1
1-2
2-3
5
1 0 7
-1
1
5
1 0-1
2
}]
5
121
254
134
1 2
2
2
i) b=
iii) b =
27. A =
29. A =
31. A =
33. A =
35. A =
38. Let A be the matrix given in Exercise 26.
a) For each vector b that follows, determine
whether b is in R(A).
b) If b is in R(A), then exhibit a vector x in R²
such that Ax = b.
ii) b =
25
c) If b is in R(A), then write b as a linear
combination of the columns of A.
-[₁
[1]
v) b = [ - ]
-6
iv) b =
12
364
01
02
03
[
vi) b =
12 3
13 1
2 2 10
2
2
6
- [8]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b2fdc56-6bb8-4ab3-bbc3-543ca3218caf%2F94f22f1a-dbb7-4902-acdf-16639da0bfc8%2Fxcwfpml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 26-37, give an algebraic specification for
the null space and the range of the given matrix A.
1-2
3
-3
6
2-6
[]
[12]
26. A =
28. A =
30. A =
32. A =
34. A =
36. A =
37. A =
1-1
2-1
13
27
1
1-2
2-3
5
1 0 7
-1
1
5
1 0-1
2
}]
5
121
254
134
1 2
2
2
i) b=
iii) b =
27. A =
29. A =
31. A =
33. A =
35. A =
38. Let A be the matrix given in Exercise 26.
a) For each vector b that follows, determine
whether b is in R(A).
b) If b is in R(A), then exhibit a vector x in R²
such that Ax = b.
ii) b =
25
c) If b is in R(A), then write b as a linear
combination of the columns of A.
-[₁
[1]
v) b = [ - ]
-6
iv) b =
12
364
01
02
03
[
vi) b =
12 3
13 1
2 2 10
2
2
6
- [8]
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