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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
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
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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
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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