ning to t .5 0 0 Define T: R³ 2. Let A = 3. A = 4. A = 5. A = In Exercises 3-6, with T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. 0-27 1 6,b= 1 -2 3 1 9. A = 3 -5 13 3 -3 6./A=0 -2 -5 0 0 0 -- 0 .5 C R³ by T(x) = Ax. Find 7(u) and 7(v). 40 -5 -7 -3 7 11. 2 -4 -9 -4 1 -3 5 4 1 -4 0 1 2 -6 1 5 , U = , b = ²3]. b = [ ²² ] b= 5 D -3 -4 6 E ,b= 7 -5 3 6 -4 a 7. Let A be a 6 x 5 matrix. What must a and b be in order to define T: Rª → Rb by T(x) = Ax? a and v = 3 -6 8. How many rows and columns must a matrix A have in order to define a mapping from R4 into R5 by the rule 7 (x) = Ax? For Exercises 9 and 10, find all x in R4 that are mapped into the zero vector by the transformation x Ax for the given matrix A.
ning to t .5 0 0 Define T: R³ 2. Let A = 3. A = 4. A = 5. A = In Exercises 3-6, with T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. 0-27 1 6,b= 1 -2 3 1 9. A = 3 -5 13 3 -3 6./A=0 -2 -5 0 0 0 -- 0 .5 C R³ by T(x) = Ax. Find 7(u) and 7(v). 40 -5 -7 -3 7 11. 2 -4 -9 -4 1 -3 5 4 1 -4 0 1 2 -6 1 5 , U = , b = ²3]. b = [ ²² ] b= 5 D -3 -4 6 E ,b= 7 -5 3 6 -4 a 7. Let A be a 6 x 5 matrix. What must a and b be in order to define T: Rª → Rb by T(x) = Ax? a and v = 3 -6 8. How many rows and columns must a matrix A have in order to define a mapping from R4 into R5 by the rule 7 (x) = Ax? For Exercises 9 and 10, find all x in R4 that are mapped into the zero vector by the transformation x Ax for the given matrix A.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
5
![1.8 EXERCISES
0
2].
1. Let A =
Find the images under T of u =
2. Let A =
- [
2
0
3. A = -2
5. A =
4. A = 0
3
6./A =
.5 0 01010
81
.5
.5
0
4 = [_-3
and define T: R² R² by T(x) = Ax.
1 0 -2]
-2 1
3 -2
0 0
L-4
C
Define T: R³ → R³ by T(x) = Ax. Find T(u) and T(v).
1-3
In Exercises 3-6, with T defined by T(x) = Ax, find a vector x
whose image under T is b, and determine whether x is unique.
-5
27
1-4, b =
-5 -9
-1
6,b= 7
L-3
1 -5 -7
[3]
u=
-3 7 5'
1
-2 1
3 -4
-4 5
011
-3 5 -4
-2
-3]. b = [²2]
, b =
67
-7
-9
1 -4 7 -5
9. A = 0 1 -4 3
2 -6 6-4
and v =
9
3
-6
9
a
[8]
b
and v =
1501
a
b
2017
7. Let A be a 6 x 5 matrix. What must a and b be in order to
define T: Rª → Rb by T(x) = Ax?
a
8. How many rows and columns must a matrix A have in order
to define a mapping from R4 into R5 by the rule T(x) = Ax?
For Exercises 9 and 10, find all x in R4 that are mapped into the
zero vector by the transformation x Ax for the given matrix A.
10. A =
11. Let b =
[1]
the range of the lin
not?
12. Let b =
3
1
0
0
1
-2 3
13. T(x)
1
b in the range of t
why not?
In Exercises 13-16, u:
5
u=
= [2]-=[-2]
mation T. (Make a sep
exercise.) Describe ge
in R².
16. T(x)
=
14. T(x) = [
u=
3
-1
4
[
15. T(x) =
(x) = [
-1
, a
5 C
0
0
0
0 -
=
- [1
0
1
0 1
C
17. Let T: R² → E
[2]
fact that T is line
3u + 2v.
into](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a737fc6-15a5-4a44-9fac-a744876436b7%2F3d8b265a-afbe-4c3c-800e-60c2ea4b310d%2Fy62s5l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.8 EXERCISES
0
2].
1. Let A =
Find the images under T of u =
2. Let A =
- [
2
0
3. A = -2
5. A =
4. A = 0
3
6./A =
.5 0 01010
81
.5
.5
0
4 = [_-3
and define T: R² R² by T(x) = Ax.
1 0 -2]
-2 1
3 -2
0 0
L-4
C
Define T: R³ → R³ by T(x) = Ax. Find T(u) and T(v).
1-3
In Exercises 3-6, with T defined by T(x) = Ax, find a vector x
whose image under T is b, and determine whether x is unique.
-5
27
1-4, b =
-5 -9
-1
6,b= 7
L-3
1 -5 -7
[3]
u=
-3 7 5'
1
-2 1
3 -4
-4 5
011
-3 5 -4
-2
-3]. b = [²2]
, b =
67
-7
-9
1 -4 7 -5
9. A = 0 1 -4 3
2 -6 6-4
and v =
9
3
-6
9
a
[8]
b
and v =
1501
a
b
2017
7. Let A be a 6 x 5 matrix. What must a and b be in order to
define T: Rª → Rb by T(x) = Ax?
a
8. How many rows and columns must a matrix A have in order
to define a mapping from R4 into R5 by the rule T(x) = Ax?
For Exercises 9 and 10, find all x in R4 that are mapped into the
zero vector by the transformation x Ax for the given matrix A.
10. A =
11. Let b =
[1]
the range of the lin
not?
12. Let b =
3
1
0
0
1
-2 3
13. T(x)
1
b in the range of t
why not?
In Exercises 13-16, u:
5
u=
= [2]-=[-2]
mation T. (Make a sep
exercise.) Describe ge
in R².
16. T(x)
=
14. T(x) = [
u=
3
-1
4
[
15. T(x) =
(x) = [
-1
, a
5 C
0
0
0
0 -
=
- [1
0
1
0 1
C
17. Let T: R² → E
[2]
fact that T is line
3u + 2v.
into
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