Linear algebra: please solve q38 correctly and handwritten In Exercises 26-37, give an algebraic specification forthe null space and the range of the given matrix A.1-23-362-6[][12]26. A =28. A =30. A =32. A =34. A =36. A =37. A =1-12-1132711-22-351 0 7-1151 0-12}]51212541341 222i) 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, determinewhether b is in R(A).b) If b is in R(A), then exhibit a vector x in R²such that Ax = b.ii) b =25c) If b is in R(A), then write b as a linearcombination of the columns of A.-[₁[1]v) b = [ - ]-6iv) b =12364010203[vi) b =12 313 12 2 10226- [8]

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Answered: 38. Let A be the matrix given in…

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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Linear algebra: please solve q38 correctly and handwritten

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]

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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