Solve the following linear system: − a π 0 + ( 1 − b ) π 1 = 0 a π 0 − π 1 + π 2 = 0 b π 1 − π 2 = 0 π 0 + π 1 + π 2 = 1 Here, π 0 , π 1 , π 2 are the variables.

Question

Solve the following linear system:                    −        a                  π          0                +        (        1        −        b        )                  π          1                =        0                            a                  π          0                −                  π          1                +                  π          2                =        0                            b                  π          1                −                  π          2                =        0                                      π          0                +                  π          1                +                  π          2                =        1            Here,       π    0    ,        π    1    ,        π    2   are the variables.

Hilfeform5c · Accepted Answer

Matrix method doesn&#039;t look so badly for me:                    a                    −        1                    1                              |                            0                            −        a                    1        −        b                    0                              |                            0                            1                    1                    1                              |                            1            Add the first row to the second and the first divided by   −  a to the third:                    a                    −        1                    1                              |                            0                            0                    −        b                    1                              |                            0                            0                                          a            +            1                    a                                                  a            −            1                    a                                      |                            1            Add the second row multiplied by             a      +      1              a      b       to the third:                    a                    −        1                    1                              |                            0                            0                    −        b                    1                              |                            0                            0                    0                                          a            −            b            +            a            b            +            1                                a            b                                                |                            1            Find       π    2  :                    a                    −        1                    1                              |                            0                            0                    −        b                    1                              |                            0                            0                    0                    1                              |                                                  a            b                                a            −            b            +            a            b            +            1                              Then       π    1  :                    a                    −        1                    1                              |                            0                            0                    1                    0                              |                                      a                      a            −            b            +            a            +            1                                              0                    0                    1                              |                                                  a            b                                a            −            b            +            a            b            +            1                              And       π    0  :                    1                    0                    0                              |                                                  1            −            b                                a            −            b            +            a            b            +            1                                              0                    1                    0                              |                                      a                      a            −            b            +            a            b            +            1                                              0                    0                    1                              |                                                  a            b                                a            −            b            +            a            b            +            1

fluerkg · Accepted Answer

If you had the first and second equations, you get the third. So, ignore the first one and consider only the other.If you don&#039;t want to use matrix, eliminate successivel variables until you end withe one equation for one unknown. Take care : may be there is a problem somewhere.

Solve the following linear system: a pi_0+(1-b) pi_1=0, a pi_0-pi_1+pi_2=0, b pi_1-pi_2=0, pi_0+p_1+p_2=1, Here, pi_0, pi_1, pi_2 are the variables.

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