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[SOLVED] 311.2.2.6 use inverse matrix to solve system of equations

karush

Well-known member
Jan 31, 2012
3,068
$\tiny{311.2.2.6}$
Use the inverse to solve the system
$\begin{array}{rrrrr}
7x_1&+3x_2&=-9\\
-2x_1&+x_2&=10
\end{array}$

$A^{-1}b=x$
$\begin{bmatrix}
\frac{1}{13}&-\frac{3}{13} \\ \\ \frac{2}{13}& \frac{7}{13} \end{bmatrix}
\begin{bmatrix}
-9\\ \\ 10
\end{bmatrix}
=
\begin{bmatrix}
-3\\ \\ 4
\end{bmatrix}$

the thing I could not get here without a calculator is $A^{-1}$
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,274
Given \(\displaystyle A = \left ( \begin{matrix} a & b \\ c & d \end{matrix} \right )\)

When all else fails:
\(\displaystyle A^{-1} = \dfrac{1}{ |A| } \left ( \begin{matrix} d & -b \\ -c & a \end{matrix} \right )\)

I have this one memorized.

-Dan
 
Last edited:

karush

Well-known member
Jan 31, 2012
3,068
ok i think i had a and switched