Question

MATRICES 2

*Necesito todo el procedimiento junto con su explicación

Answer 1

2A = AX + B 

2A - B = AX

$2A - B = A ^{-1} *A *X$

$A ^{-1} (2A-B) = X$

$2A = 2 \left[\begin{array}{ccc}1&0\\-1&1\\\end{array}\right] = \left[\begin{array}{ccc}2&0\\-2&10\\\end{array}\right]$

$2A-B = \left[\begin{array}{ccc}2&0\\-2&2\\\end{array}\right] - \left[\begin{array}{ccc}-1&2\\-3&1\\\end{array}\right] = \left[\begin{array}{ccc}3&-2\\1&1\\\end{array}\right]$

$A ^{-1} = \frac {(A ^{*} )^{t} }{DetA}$

Det A = (1*1 - 0)
Adjunta de A = 
Eliminamos fila 1 columna 1  y queda 1
Eliminamos fila 1 columna 2  y queda -1
Eliminamos fila 2 columna 1 y queda 0
Eliminamos fila 2 columna 2 y queda 1

respetamos$\left[\begin{array}{ccc}+&-\\-&+\\\end{array}\right]$

$\left[\begin{array}{ccc}1&1\\0&1\\\end{array}\right]$

transponemos
$\left[\begin{array}{ccc}1&0\\1&1\\\end{array}\right]$

$A ^{-1} = \frac{ \left[\begin{array}{ccc}1&0\\1&1\\\end{array}\right] }{1}$

$A ^{-1} = \left[\begin{array}{ccc}1&0\\-1&1\\\end{array}\right]$

$X=A ^{-1}*(2A-B)= \left[\begin{array}{ccc}1&0\\1&1\\\end{array}\right] * \left[\begin{array}{ccc}3&-2\\1&1\\\end{array}\right] =$



$x = \left[\begin{array}{ccc}3&-2\\4&-1\\\end{array}\right]$

(1*3 +0*1) = 3        -2 = (1*-2+0*1)
(1*3+1*1) = 4         -1 = (1*-2+1*1)