#13 11:34Done elementary_linear_algebra_8th_...2.2 Exercises Se Calcchat.com tor worked out sclutons to od-numbered exercises.Associativity of Matrix Multiplication In Exercises 23and 24, find the matrix product ABC by (a) groupingthe factors as (AB)C, and (b) grouping the factors asA(BC). Show that you obtain the same result fromboth processes.Evaluating an Expression In Exercises 1-6, evaluatethe expression.-10142.23. A - ; -: c-; 124. A - [ -BI -5-6B34. (15 -2 4 o1 + (140] +6 -1891)-3C-5.-5Noncommutativity of Matrix Multiplication InExercises 25 and 26, show that AB and BA are not equalfor the given matrices.34 +-9136Operations with Matrices In Exercises 7-12, performthe operations, given a = 3, b = -4, and25. A = 8-: 926. A-B-7. aA + bB8. A +B10. (a + biBEqual Matrix Products In Exercises 27 and 28, showthat AC = BC, even though A + B.9. abB)11. (a - bA - B)12. (ab)o27. A - | -: c-[; |B13. Solve for X in the equation, given328. A =0 524-6-3-5 and B-4. BA=-24-1[3 -2o 0 0C-0 04 -2-344(a) 3X + 24-R(b) 24- SR- Y(c) X - 34 + 2B = 0 (d) 6X - 44 - 3B = 0314. Solve for X in the equation, given-2 -1I 0 and B = 23 -4Zero Matrix Product In Exercises 29 and 30, show thatAB = 0, even though AO and B+ 0.3.B---4 -129. A =and B=(a) X- 34 - 28(b) 2X = 2A -R(e) 2X + 3A = B(d) 24 + 48 --2X30. A =and B=Operations with Matrices In Exercises 15-22,perform the operations, given e = -2 andOperations with Matrices In Exercises 31-36,perform the operations whenA -: : -: 1c - [; }A =! 2115. (BA)16. (CB)31. IA32. AI17. B(CA)18. CIRCY33. AI + A)34. A+ IA19. (B + C)A20. B(C + 0)35. A36. 421. cB(C + C)22. B(CA)C Cl pmaltycoking C60Chapter 2 MatricesWriting In Exercises 37 and 38, explain why theformula is not valid for matrices. Illustrate yourargument with examples.Finding an nth Root of a Matrix In Exercises 53and 54, find the nth root of the matrix B. An nth root ofa matrix R is a matrix A such that 4 = B.[953. B-. n-237. (A + B)IA - B) - A-838. (A + B)(A + B) - A + 2AB + BFinding the Transpose of a Matrix In Exercises 39and 40, find the transpose of the matrix.854. B-0 -127ol -36 -7 1940. D=-7 o 2319 23 - 3239. D--3True or False? In Exercises 55 and 56, determinewhether each statement is true or false. If a statementFinding the Transpose of a Product of Two MatricesIn Exercises 41-44, verify that (AB) = B'A".is true, give a reason or cite an appropriate statementfrom the text. f a statement is false, provide an examplethat shows the statement is not true in all cases or cite an-3appropriate statement from the text.55. (a) Matrix addition is commutative.41. A=and =-1(b) The transpose of the product of two matrices equalsthe product of their transposes; that is, (AB) - A'B(c) For any matrix C the matrix CC' is symmetric.56. (a) Matrix multiplication is commutative.42. A - 3 and B-and B- 3!(b) If the matrices A. B, and C satisfy AB - AC, then

Name: #13 11:34Done elementary_linear_algebra_8th_...2.2 Exercises Se Calcch
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #13 11:34Done elementary_linear_algebra_8th_...2.2 Exercises Se Calcchat.com tor worked out sclutons to od-numbered exercises.Associativity of Matrix Multiplication In Exercises 23and 24, find the matrix product ABC by (a) groupingthe factors as (AB)