Math Is Fun Forum

paul.j

Guest

Martix Equations

Find X

4   -3   X  =    16   -40
9   -6             27   -84

The numbers would be in brackets can any one help

jacs

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Martix Equations

One way to do this would be to create an augmented matrix and then use elementary row operations to make the left side become the identity matrix. Then the right side would be X.

4  -3  |  16  -40
9  -6  |  27  -84

Take half of row 2 from row 1:
-0.5  0  |  2.5  2
  9   -6  |  27  -84

Divide row 1 by -0.5:
1   0   |   -5   -4
9  -6   |  27   -84

Take 9 of row 1 from row 2:
1   0   |   -5   -4
0  -6   |   72  -48

Divide row 2 by -6:
1  0  |  -5    -4
0  1  |  -12   8

The left side is now the identity, which means that X has to be (-5   -4)
                                                                                          (-12  4).

Checking by putting this into the original equation shows that this is the right answer.

Another way of doing it would be to multiply both sides by the inverse of what X is premultiplied by, but that usually takes longer.

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It wanted to be normal.