Exercises 1-11 refer to the vectors in Eq. (14). 2 -2 b= 2 --[-]· ·-[3] [3] -[8] - [8] d (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} 2. S = {b} 3. S = {e} 4. S = (a, b) 5. S = (a, d} 6. S = {a, c)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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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
Transcribed Image Text: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
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