Question

3 | 3 | are particular solutions to the system 2 14 6x3. (b) Find the general solution. 3 2 -4

Answer 1

Given system is A X = B A = [2 1 3 - 1 - 4 2 - 5 - 8 - 4] X = [x_1 x_2 x_3] B = [1 - 3 5] consider the argument matrix A system [A/B] = [2 1 3 - 1 - 4 2 - 5: - 6: - 4: 1 - 3 5] Now, apply the row operators on [A/B] until [A/B] reduced to echelon from R_1 leftrightarrow R_2 sim [1 3 3 - 4 - 1 2 - 8 - 5 - 4 - 3 1 5] R_2 rightarrow R-2 - 2r_1, R_3 rightarrow R_3 - 3R-1 sim [1 0 0 - 4 7 14 - 6 7 14 - 3 7 14] R_3 rightarrow R_3 - 2R_2 and R_2 rightarrow R_2/7 \r\n sim [1 0 0 - 4 1 0 - 6 1 0 - 3 1 0] this is in echelon form The number of non zeros in A and [A/B] is 2 Rightarrow rank (A) = rank (A/B) = 2