Some Special Matrix Products Let A be an m×n matrix.8.-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 simplifyA.-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 matrixExercises:)-2-1In Exercises 1 – 4 determine whether or not the matrix prod-ucts 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 =-2118 050 1-53. А —and B =-13-1-3 0-103Let A' is the transpose of the matrix A, as defined in Sec-tion 1.3. Compute AA".1-5

Name: Some Special Matrix Products Let A be an m×n matrix.8.-1Then4.Answer:
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Description: Some Special Matrix Products Let A be an m×n matrix.8.-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