Solve the following system of equations by using the inverse of the coefficient matrix A. (AX = B) x + 5y= - 10, -2x+7y=-31

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umshikepl · Accepted Answer

A          −      1        =      1                  |            A              |              a  d  j  A  =      1    17        [                            7                          −          5                                      2                          1                      ]    =      [                                        7            17                                                              −              5                        17                                                            2            17                                                1            17                                ]  AX=B  X  =      A          −      1        B      (                            x                                      y                      )    =      (                                        85            17                                                                          −              51                        17                                )    =      (                            5                                      −          3                      )

on2t1inf8b · Accepted Answer

A  X  =  B  ⇒  X  =  A  −  1  B  A  =  ,  B  =      (                            −          10                                      −          31                      )   and X=      A          −      1        =            (                                    7                                −            5                                                2                                1                              )        17  if   A  =      (                            a                          b                                      c                          d                      )    t  h  e  n         A          −      1        =            (                                    d                                −            b                                                −            c                                a                              )              |                                    a                                b                                                c                                d                              |            (                            1                          5                                      −          2                          7                      )        (                            x                                      y                      )    =      (                            −          10                                      −          31                      )    ⇒=      (                                        7            17                                                              −              5                        17                                                            2            17                                                1            17                                )        (                            −          10                                      −          31                      )    ⇒      (                            −                      70            17                    +                      155            17                                                −                      20            17                    −                      31            17                                )    ⇒      (                                        85            17                                                                          −              51                        17                                )    =      (                            5                                      −          3                      )

Solve the following system of equations by using the inverse of the coefficient matrix A. (AX = B) x + 5y= - 10, -2x+7y=-31

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