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5. A = -1 2 5 4 2-3 3 [21] -2 B = =

5. A = -1 2 5 4 2-3 3 [21] -2 B = =

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
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2 0 A = [² -3 -2] 4 -5 c = [| 2.1 EXERCISES In Exercises I and 2, compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let 2]. 1. -2A, B - 2A, AC, CD 1 -2 A = 3. Let A = -[- 1 B = [1 ] -4 -3 3 -1 D = 4 =[$ =2]. Compute 5 -2 2. Let A be a 4 x 4 matrix and let x be a vector in R4. What is the fastest way to compute A²x? Count the multiplications. -2 4] T Compute (Ax), xTAT, xx", and xTx. Is ATx" defined? 9 3. Suppose A is an m x n matrix, all of whose rows are identical. Suppose B is an n x p matrix, all of whose columns are identical. What can be said about the entries in AB FLAATIO -5 2. A + 2B, 3C - E, CB, EB In the rest of this exercise set and in those to follow, you should assume that each matrix expression is defined. That is, the sizes of the matrices (and vectors) involved "match" appropriately. 5 $]. E = [3] 4 4 Compute A-513 and (513) A, when 9 -1 3 -8 7 -6 -4 1 8 Compute 312 - A and (31₂) A. In Exercises 5 and 6, compute the product AB in two ways: (a) by the definition, where Ab, and Ab2 are computed separately, and (b) by the row-column rule for computing AB. 5. A = = COMUN 5 2 4 -3 -2 0 6. A 3 5 2 4 -3 10. Let A , B = H 11. Let A = = 3-2 -2 © M3R03H1 7. If a matrix A is 5 × 3 and the product AB is 5 x 7, what is the size of B? 2 -3 · B = [ ²2 - [23] 8. How many rows does B have if BC is a 3 x 4 matrix? 2 5 V [ - ] and B = [₁ ] Let A 4 -5 3 k -3 1 k, if any, will make AB = BA? = -[- ³ ] ₁ B = [ $ $]. 5 5 -4 Verify that AB = AC and yet BC. 8 4 13] 20 5 and D= = What value(s) of [2 and C = - [5 3 - 1 1 1 2 1 4 pute AD and DA. Explain how the columns or rows of A change when A is multiplied by D on the right or on the left. Find a 3 x 3 matrix B, not the identity matrix or the zero matrix, such that AB = BA. 0 0 030 0. Com- 005 Exerci which the ir statement Tr 15. a. If A res b. Eac of C. d. e. 16./a. A b. A ΤΙ C. d. O e. If 17. If th 18. Su M W V 19. S 20. 20
Transcribed Image Text:2 0 A = [² -3 -2] 4 -5 c = [| 2.1 EXERCISES In Exercises I and 2, compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let 2]. 1. -2A, B - 2A, AC, CD 1 -2 A = 3. Let A = -[- 1 B = [1 ] -4 -3 3 -1 D = 4 =[$ =2]. Compute 5 -2 2. Let A be a 4 x 4 matrix and let x be a vector in R4. What is the fastest way to compute A²x? Count the multiplications. -2 4] T Compute (Ax), xTAT, xx", and xTx. Is ATx" defined? 9 3. Suppose A is an m x n matrix, all of whose rows are identical. Suppose B is an n x p matrix, all of whose columns are identical. What can be said about the entries in AB FLAATIO -5 2. A + 2B, 3C - E, CB, EB In the rest of this exercise set and in those to follow, you should assume that each matrix expression is defined. That is, the sizes of the matrices (and vectors) involved "match" appropriately. 5 $]. E = [3] 4 4 Compute A-513 and (513) A, when 9 -1 3 -8 7 -6 -4 1 8 Compute 312 - A and (31₂) A. In Exercises 5 and 6, compute the product AB in two ways: (a) by the definition, where Ab, and Ab2 are computed separately, and (b) by the row-column rule for computing AB. 5. A = = COMUN 5 2 4 -3 -2 0 6. A 3 5 2 4 -3 10. Let A , B = H 11. Let A = = 3-2 -2 © M3R03H1 7. If a matrix A is 5 × 3 and the product AB is 5 x 7, what is the size of B? 2 -3 · B = [ ²2 - [23] 8. How many rows does B have if BC is a 3 x 4 matrix? 2 5 V [ - ] and B = [₁ ] Let A 4 -5 3 k -3 1 k, if any, will make AB = BA? = -[- ³ ] ₁ B = [ $ $]. 5 5 -4 Verify that AB = AC and yet BC. 8 4 13] 20 5 and D= = What value(s) of [2 and C = - [5 3 - 1 1 1 2 1 4 pute AD and DA. Explain how the columns or rows of A change when A is multiplied by D on the right or on the left. Find a 3 x 3 matrix B, not the identity matrix or the zero matrix, such that AB = BA. 0 0 030 0. Com- 005 Exerci which the ir statement Tr 15. a. If A res b. Eac of C. d. e. 16./a. A b. A ΤΙ C. d. O e. If 17. If th 18. Su M W V 19. S 20. 20
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