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[2 8 2. Given A = 3 0,8 Ls 1 7 27 and C = 6 3 3 8 (a) Is AB defined? Calculate AB. Can you calculate BA? Why? (b) Is BC defined? Całculate BC. Is CB defined? If so, catculate CB. Is it true that BC = CB?

[2 8 2. Given A = 3 0,8 Ls 1 7 27 and C = 6 3 3 8 (a) Is AB defined? Calculate AB. Can you calculate BA? Why? (b) Is BC defined? Całculate BC. Is CB defined? If so, catculate CB. Is it true that BC = CB?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Ath Fundamental Methods of Mathem... i = 1, 2, ..., m l;= 1,2, 11 This last equation represents yet another way of stating the rule of multiplication for the matrices defined above. EXERCISE 4.2 [8 3 find: 6 1 [7 -1 1. Given A = 8 = 6. and C = (C) 3A (b) C - A [2 87 2. Given A = 3 01,8 = 5 1 (d) 4B + 2 [2 0 , and C = (a) Is AB defined? Calculate AB. Can you calculate BA? Why? (b) Is BC defined? Całculate BC. Is CB defined? If so, całculate CB. Is it true that BC= CB? calculate the product. In this case do we have AB = BA? 4. Find the product matrices in the following (in each case, append beneath every matrix a dimension indicator): O 2 01[8 0 (a) 3 0 4 0 1 2 3 0 L3 5 (c) 2 -7 4 -11 6 5 -1 (b) 1 0 (d) [a b c] 0 2 1 4 2 4 5. In Example 7, if we arrange the quantities and prices as column vectors instead of row vectors, is Q- P defined? Can we express the total purchase cost as Q P? As Q' - P? As Q.P'? 6. Expand the following summation expressions: (a) xi 2 ( ax- i=1 i-s (c) bx, Chapter 4 Lineur Models and Marrix Algebra 59 7. Rewrite the foltowing in E notation: (0) x1 (X1 – 1) + 2x2{x2 – 1) + 3x3(x3 – 1) (b) az{x3 + 2) + a3(X4 + 3) + C4(xs + 4) 1 1 (c) - + (x + 0) 1 1 (d) 1+ x x2 (x # 0) + 8. Show that the foliowing are true: n-1 (a) + Xn+1 = E X; (b) E ab, Y; = a (c) E (x; + y,) = E x; + 4.3 Notes on Vector Operations In Secs. 4.1 and 4.2, vectors are considered as a special type of matrix. As such, they qual- ify for the appiication of all the algebraic operations discussed. Owing to their dimensional nesuliarities k addirional comment
Transcribed Image Text:Ath Fundamental Methods of Mathem... i = 1, 2, ..., m l;= 1,2, 11 This last equation represents yet another way of stating the rule of multiplication for the matrices defined above. EXERCISE 4.2 [8 3 find: 6 1 [7 -1 1. Given A = 8 = 6. and C = (C) 3A (b) C - A [2 87 2. Given A = 3 01,8 = 5 1 (d) 4B + 2 [2 0 , and C = (a) Is AB defined? Calculate AB. Can you calculate BA? Why? (b) Is BC defined? Całculate BC. Is CB defined? If so, całculate CB. Is it true that BC= CB? calculate the product. In this case do we have AB = BA? 4. Find the product matrices in the following (in each case, append beneath every matrix a dimension indicator): O 2 01[8 0 (a) 3 0 4 0 1 2 3 0 L3 5 (c) 2 -7 4 -11 6 5 -1 (b) 1 0 (d) [a b c] 0 2 1 4 2 4 5. In Example 7, if we arrange the quantities and prices as column vectors instead of row vectors, is Q- P defined? Can we express the total purchase cost as Q P? As Q' - P? As Q.P'? 6. Expand the following summation expressions: (a) xi 2 ( ax- i=1 i-s (c) bx, Chapter 4 Lineur Models and Marrix Algebra 59 7. Rewrite the foltowing in E notation: (0) x1 (X1 – 1) + 2x2{x2 – 1) + 3x3(x3 – 1) (b) az{x3 + 2) + a3(X4 + 3) + C4(xs + 4) 1 1 (c) - + (x + 0) 1 1 (d) 1+ x x2 (x # 0) + 8. Show that the foliowing are true: n-1 (a) + Xn+1 = E X; (b) E ab, Y; = a (c) E (x; + y,) = E x; + 4.3 Notes on Vector Operations In Secs. 4.1 and 4.2, vectors are considered as a special type of matrix. As such, they qual- ify for the appiication of all the algebraic operations discussed. Owing to their dimensional nesuliarities k addirional comment
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