2 x − 3 y + 4 z = − 19 6 x + 4 y − 2 z = 8 x + 5 y + 4 z = 23what I have done so far is I put the nubmer and x,y and z in matrix form: [ 2 − 3 4 6 4 − 2 1 5 4 ] [ x y z ] = [ − 19 8 23 ]

Question

2  x  −  3  y  +  4  z  =  −  19    6  x  +  4  y  −  2  z  =  8    x  +  5  y  +  4  z  =  23what I have done so far is I put the nubmer and x,y and z in matrix form:      [                            2                          −          3                          4                                      6                          4                          −          2                                      1                          5                          4                      ]        [                            x                                      y                                      z                      ]    =      [                            −          19                                      8                                      23                      ]

Hugo Bruce · Accepted Answer

You can use Gaussian Elimination on the augmented coefficient matrix to solve for   x  ,  y  ,  z by expressing the matrix in reduced row echelon form.      [                            2                          −          3                          4                          ∣                          19                                      6                          4                          −          2                          ∣                          8                                      1                          5                          4                          ∣                          23                      ]  If you do this correctly, you should obtain the following:      [                            1                          0                          0                          ∣                          20                  /          9                                      0                          1                          0                          ∣                          7                  /          9                                      0                          0                          1                          ∣                          38                  /          9                      ]  This means that      [                            x                                      y                                      z                      ]    =      [                            20                  /          9                                      7                  /          9                                      38                  /          9                      ]

Ashly Harrell · Accepted Answer

You can also use Cramer&#039;s Rule:  x  =            |                                                  −              19                                            −            3                                4                                                              8                                            4                                −            2                                                              23                                            5                                4                              |              |                                    2                                −            3                                4                                                6                                4                                −            2                                                1                                5                                4                              |        =  −  2  y  =            |                                    2                                              −              19                                            4                                                6                                              8                                            −            2                                                1                                              23                                            4                              |              |                                    2                                −            3                                4                                                6                                4                                −            2                                                1                                5                                4                              |        =  5  z  =            |                                    2                                −            3                                              −              19                                                            6                                4                                              8                                                            1                                5                                              23                                          |              |                                    2                                −            3                                4                                                6                                4                                −            2                                                1                                5                                4                              |        =  0In the numerator, replace the column in the matrix corresponding to the given variable by the column of results. Note that the bars denote the determinant of the matrix.

2 x − 3 y + 4 z = − 19 <mspac

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