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In Exercises 1-12, find the products AB and BA to determine whether B is the multiplicative inverse of A.
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Algebra and Trigonometry (6th Edition)
- The multiplicative inverse of 1 + 3x in Z,[x] is: 4x+1 O 6x+1arrow_forwardLet -1] 4 k 0 0 2 -k 2 k- 4] A = -2 B = 4 -1 -2 0 k-8 i Express AB in the simplest form ii Find the inverse of A in terms of k, stating the condition under which A-1 existarrow_forwardUse Gauss-Jordan method to calculate the inverse of A 1 A =| 0 1 1 1 1 1arrow_forward
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- PLEASE TYPE ONLY*** Exercise 4.2.3: Find a counterexample. Find a counterexample to show that each of the statements is false. (d) Every positive integer can be expressed as the sum of the squares of two integers. (e) The multiplicative inverse of a real number x, is a real number y such that xy = 1. Every real number has a multiplicative inverse.arrow_forwardUse the column-viewpoint to compute the product C = AB of [1 A = 1 LO -11 1 2 and B [2 =[²₂9] hods)arrow_forward(5.1) Compute the product AB for 10-1 1 20-1 A= -1 3 and B= 0-2 1 -1 2 2 1 -1 (5.2) Use your answer in (5.1) to verify that det(AB) = det(A) det(B). (5.3) Determine whether each equality det(AB) = det(A) det(B) and det(A-¹ + B-¹) = det(A)+det(B) holds. det(AB)arrow_forward
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