Linear algebra: please solve q5 and 18 correctly and handwritten Exercises 1-11 refer to the vectors in Eq. (14).2--[4] »-[3] [3]a =b =-12d=-[8] - [8]e=C=(14)In Exercises 1-11, either show that Sp(S) = R² or givean algebraic specification for Sp(S). If Sp(S) # R²,then give a geometric description of Sp (S).1. S = {a}4. S= (a, b)2. S = {b}5. S = {a, d)3. S= {e}6. S = {a, c}In Exercises 12-19, either show that Sp(S) = R³ or givean algebraic specification for Sp(S). If Sp(S) # R³,then give a geometric description of Sp(S).12. S = {v}13. S = {w}14. S = {v, w}16. S18. S{v, w, x}{v, w, z}15. S = (v, x}17. S = {w, x, z}19. S = {w, x, y}7. S = (b, e)9. S = {b, c, d}11. S {a, c, e}Exercises 12-19 refer to the vectors in Eq. (15).-0-0-0W =1V = 2y =26. A =28. A =Z=-38. S = {a, b, d}10. S (a, b, e}13.3 Examples of Subspaces[:]In Exercises 26-37, give an algebraic specification forthe null space and the range of the given matrix A.1-26-1 32-62X =27. A =29. A =(15)2 5187

According to guidelines we can solve only first one mentioned question.

Answered: Exercises 1-11 refer to the vectors 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 q5 and 18 correctly and handwritten

Exercises 1-11 refer to the vectors in Eq. (14).
2
--[4] »-[3] [3]
a =
b =
-1
2
d=
-[8] - [8]
e=
C=
(14)
In Exercises 1-11, either show that Sp(S) = R² or give
an algebraic specification for Sp(S). If Sp(S) # R²,
then give a geometric description of Sp (S).
1. S = {a}
4. S= (a, b)
2. S = {b}
5. S = {a, d)
3. S= {e}
6. S = {a, c}
In Exercises 12-19, either show that Sp(S) = R³ or give
an algebraic specification for Sp(S). If Sp(S) # R³,
then give a geometric description of Sp(S).
12. S = {v}
13. S = {w}
14. S = {v, w}
16. S
18. S
{v, w, x}
{v, w, z}
15. S = (v, x}
17. S = {w, x, z}
19. S = {w, x, y}
7. S = (b, e)
9. S = {b, c, d}
11. S {a, c, e}
Exercises 12-19 refer to the vectors in Eq. (15).
-0-0-0
W =
1
V = 2
y =
26. A =
28. A =
Z=
-3
8. S = {a, b, d}
10. S (a, b, e}
1
3.3 Examples of Subspaces
[:]
In Exercises 26-37, give an algebraic specification for
the null space and the range of the given matrix A.
1-2
6
-1 3
2-6
2
X =
27. A =
29. A =
(15)
2 5
187

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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