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help i need to convert a matrix to an idendity matrix the matrix is 2 9 -4        THANK YOU

                                                                                                       3 5 1

                                                                                                       2 3 -2

 Sep 1, 2015
 #1
avatar+128732 
+5

2   9   -4        1    0    0

3   5    1         0   1    0

2   3   -2        0    0    1        multiply the 1st row by 1/2

 

1  9/2   -2       1/2  0   0

3   5      1        0   1   0

2   3     -2        0    0   1      multiply the 1st row by -3   add this to the 2nd row

 

1     9/2   - 2        1/2  0   0

0  -17/2    7        -3/2  1   0 

2     3      -2          0    0   1      multiply the the 1st row by -2 add this to the 3rd row

 

 

1     9/2    -2          1/2   0   0

0   -17/2   7           -3/2  1   0

0    -6       2           -1     0   1    multiply the first two rows by 2

 

2    9      -4             1   0   0

0   -17    14           -3   2   0

0   -6       2            -1  0    1        multiply the 2nd row by 9/17  add to the 1sr row 

 

2   0    58/17         -10/17   18/17   0

0  -17    14            -3            2        0

0  -6       2             -1            0        1      multiply the 2nd row by -6/17 add to the 3rd row

 

2   0    58/17         -10/17   18/17    0

0   -17   14             -3             2       0

0    0   -50/17        1/17      -12/17   1   multply the 1st and 3rd rows by 17

 

 

34   0   58             -10     18      0

0  -17  14                -3      2       0

0   0   -50                1    -12     17      multiply the 3rd row by 58/50  add to the 1st row

 

34   0   0            -221/25   102/25   493/25

0   -17  14              -3           2           0

0    0   -50               1          -12        17       multiply the 3rd row by 14/50  add to the 2nd row

 

34   0   0          -221/25    102/25    493/25

0   -17  0            - 68/25     -34/25    119/25

0   0    -50             1           -12          17        

 

divide the 1st row by 34, the 2nd by -17,  and the 3rd by   -50

 

1  0  0            -13/50    3/25    29/50

0  1  0               4/25    2/25    -7/25

0  0  1              -1/50    6/25     -17/50 

 

The first matrix is the identity of your matrix.......the second matrix is the inverse of your matrix.....

 

 

cool cool cool

 Sep 1, 2015
 #2
avatar+128732 
0

2   9   -4        1    0    0

3   5    1         0   1    0

2   3   -2        0    0    1        multiply the 1st row by 1/2

 

1  9/2   -2       1/2  0   0

3   5      1        0   1   0

2   3     -2        0    0   1      multiply the 1st row by -3   add this to the 2nd row

 

1     9/2   - 2        1/2  0   0

0  -17/2    7        -3/2  1   0 

2     3      -2          0    0   1      multiply the the 1st row by -2 add this to the 3rd row

 

 

1     9/2    -2          1/2   0   0

0   -17/2   7           -3/2  1   0

0    -6       2           -1     0   1    multiply the first two rows by 2

 

2    9      -4             1   0   0

0   -17    14           -3   2   0

0   -6       2            -1  0    1        multiply the 2nd row by 9/17  add to the 1sr row 

 

2   0    58/17         -10/17   18/17   0

0  -17    14            -3            2        0

0  -6       2             -1            0        1      multiply the 2nd row by -6/17 add to the 3rd row

 

2   0    58/17         -10/17   18/17    0

0   -17   14             -3             2       0

0    0   -50/17        1/17      -12/17   1   multply the 1st and 3rd rows by 17

 

 

34   0   58             -10     18      0

0  -17  14                -3      2       0

0   0   -50                1    -12     17      multiply the 3rd row by 58/50  add to the 1st row

 

34   0   0            -221/25   102/25   493/25

0   -17  14              -3           2           0

0    0   -50               1          -12        17       multiply the 3rd row by 14/50  add to the 2nd row

 

34   0   0          -221/25    102/25    493/25

0   -17  0            - 68/25     -34/25    119/25

0   0    -50             1           -12          17        

 

divide the 1st row by 34, the 2nd by -17,  and the 3rd by   -50

 

1  0  0            -13/50    3/25    29/50

0  1  0               4/25    2/25    -7/25

0  0  1              -1/50    6/25     -17/50 

 

The first matrix is your matrix transformed to an identity matrix.......the second matrix is the inverse of your matrix.....

 

 

cool cool cool

 Sep 1, 2015
 #3
avatar+128732 
0

Disregard the first answer.....this statement isn't quite correct... "The first matrix is the identity of your matrix"

The second answer is better......!!!!  ......"The first matrix is your matrix transformed to an identity matrix"

 

cool cool cool

 Sep 1, 2015

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