Inverse matrix (to solve a linear system of equations)

FMMurphy

Junior Member
Joined
Mar 12, 2006
Messages
51
I am to solve the linear system using an inverse matrix. The problem is:

. . .5x + 6y = 14
. . .4x - . .y = 17

The determinant would be:

. . .| 5. ..6 |
. . .| 4. .-1 |

This would then be 1 / (-5 - 24) = 1 / (-29). Then the inverse would be:

. . .-1. ..-6. . .[ 14 ]
. . .-4. . .5. .. [. .7 ]

I used the calculator and got:

. . .[ -51 ]
. . .[ -21 ]

But this doesn't look right!
_________________________________
Edited by stapel -- Reason for edit: restoring formatting
 
\(\displaystyle \left[ {\begin{array}{rr}
5 & 6 \\
4 & { - 1} \\
\end{array}} \right]^{ - 1} = \left[ {\begin{array}{rr}
{\frac{1}{{29}}} & {\frac{6}{{29}}} \\
{\frac{4}{{29}}} & {\frac{{ - 5}}{{29}}} \\
\end{array}} \right]\)
 
It's difficult to follow what you posted. Take the time to learn some LaTex if you plan on posting frequently.

The inverse of a 2X2 matrix is given by:

\(\displaystyle \L\\A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}\)

Run your numbers and you should get what pka posted.
 
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