The solution by Cramer's rule to the linear system a\\X\ + 012*2 + 013*3 = b\, 021*1 + 022*2 + 023*3 = bi, 031*1 + 032*2 + 033*3 = ^3. has a. b. c. d. e. a. b. *1 = det and *3 = det D b] a12 "13 hi 22 "23 b-s "32 "33 ii "12 b\ 2I "22 hi 3I "32 h D\ I , *2 = det D D on 021 031 ^3 D where D det b\ "13 hi "23 = hi "33 "11 "12 "13 "21 "22 "23 "31 "32 "33 D2 D Find the solution to the linear system 2*| + 3*2 *3 = 4, *1 2*2 + *3 = 6, *1 12*2 + 5*3 = 10, by Cramer's rule. Show that the linear system 2*| + 3*2 *3=4, *1 2*2 + *3 = 6, *1 12*2 + 5*3 = 9, does not have a solution. Compute D\, D2, and D3. Show that the linear system 2*| 4- 3*2 *3 = 4, *1 2*2 + *3 = 6, *1 12*2 + 5*3 = 10, has an infinite number ofsolutions. Compute D\, D2, and D3. Prove that if a 3 x 3 linear system with Z) = 0 has solutions, then D\ = >2 = O3 = 0. Determine the number of multiplications/divisions and additions/subtractions required for Cramer's rule on a 3 x 3 system.

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