ExercisesT: R² → R² defined bv T(x1. r2)= (r, + xɔ. X1 – Xn – 1).8Some Special Matrix Products Let A be an m×n matrix.-1Then4.Answer:A-312and-428-3OA141AO-56.7-20AlnAIm AIn Exercises 5 – 8 compute the given matrix product.)(3-11The first two equalities are easily checked using (3.5.3).It is not significantly more difficult to verify the last twoequalities using (3.5.3), but we shall verify these equali-ties using the language of linear mappings, as follows:5.1-33136.-2-23-11-1LAI, (x) = LALI,(x) = LA(x),231237.-2since LI, (x) = x is the identity map. Therefore AInA similar proof verifies that ImAverification of these equalities using the notions of linearmappings may appear to be a case of overkill, the nextsection contains results where these notions truly simplifyА.-23-11-1A. Although the%3D2-13178.15-2-11-1-53the discussion.9. Determine all the 2 × 2 matrices B such that ABВАwhere A is the matrixExercisesA = (; ;).-14 determine whether or not the matrix prod-In Exercises 1ucts AB or BA can be computed for each given pair of ma-trices A and B. If the product is possible, perform the com-putation.10. Leta3A =1andВ -4210.-21. А —and B =For which values of a and b does AB = BA?%3D-213-1-21211. Let2. А —4and B10-11-3A =-21128 0230 1-53. А —and B =-13-1-3-103Let A' is the transpose of the matrix A, as defined in Sec-tion 1.3. Compute AA'.1-5

Name: ExercisesT: R² → R² defined bv T(x1. r2)= (r, + xɔ. X1 – Xn – 1).8Som
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Description: ExercisesT: R² → R² defined bv T(x1. r2)= (r, + xɔ. X1 – Xn – 1).8Some Special Matrix Products Let A be an m×n matrix.-1Then4.Answer:A-312and-428-3OA141AO-56.7-20AlnAIm AIn Exercises 5 – 8 compute the given matrix product.)(3-11The first two equalit

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Answered: -1 4. Answer: A -3 12 and В %3D -4 8 -3…

Math

Algebra

-1 4. Answer: A -3 12 and В %3D -4 8 -3 1 4 1 -5 6. -20

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.FOM: Focus On Modeling: Computer Graphics

Problem 2P: Verify that multiplication by the given matrix has the indicated effect when applied to the gray...

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