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Resolver la siguiente ecuación matricial: <div><br /></div><div style="text-align: center; ">A<sup>-1</sup>XB - 2CD = B<sup>2</sup></div><div style="text-align: center; "><br /></div><div style="text-align: left; ">Siendo A = #A, B = #B, C = #C y D = #D.</div><div style="text-align: center; "><br /></div><div>E indicar en el recuadro de abajo la matriz X (sólo introduce a matriz, no escribas X=).</div>
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SOLUCIÓN:<div><br /></div><div>Despejamos de la ecuación matricial. En primer lugar dejamos las expresiones donde esté la matriz incógnita en un lado de la igualdad:</div><div style="text-align: center; "><br /></div><div style="text-align: center; "> <span style="text-align: center; ">A</span><sup style="text-align: center; ">-1</sup><span style="text-align: center; ">XB = B</span><sup style="text-align: center; ">2</sup><span style="text-align: center; "> + </span><span style="text-align: center; ">2CD</span></div><div style="text-align: justify; "><br /></div><div style="text-align: justify; ">Y para dejar la matriz X sola , debemos multiplicar <span style="text-align: center; "> </span><span style="text-align: center; ">A</span><sup style="text-align: center; ">-1</sup><span style="text-align: center; ">XB por A por la izquierda y por B<sup>-1</sup> por la derecha. Esto debe hacerse en ambos miembros, para que se mantenga la igualdad.</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: left; "><span style="text-align: center; "> A</span><span style="text-align: center; ">A</span><sup style="text-align: center; ">-1</sup><span style="text-align: center; ">XBB<sup>-1</sup> = A(B</span><sup style="text-align: center; ">2</sup><span style="text-align: center; "> + </span><span style="text-align: center; ">2CD)B<sup>-1</sup></span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">Queda entonces: </span><span style="text-align: center; ">X = A(B</span><sup style="text-align: center; ">2</sup><span style="text-align: center; "> + </span><span style="text-align: center; ">2CD)B<sup>-1</sup></span></div><div style="text-align: justify; "><span style="text-align: center; "><sup><br /></sup></span></div><div style="text-align: justify; "><span style="text-align: center; ">Sólo queda ir calculando las matrices:</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">B<sup>2</sup>= #B2</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">2CD= #CD</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">B<sup>2</sup>+2CD = #B2CD</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">A(B</span><sup style="text-align: center; ">2</sup><span style="text-align: center; ">+2CD) = #AB2CD</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">B<sup>-1</sup>= #BINV</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">A(B</span><sup style="text-align: center; ">2</sup><span style="text-align: center; ">+2CD)</span><span style="text-align: center; ">B</span><sup style="text-align: center; ">-1</sup><span style="text-align: center; "> = #X</span></div><div style="text-align: justify; "><span style="text-align: center; "><br /></span></div><div style="text-align: justify; "><span style="text-align: center; ">Y esta última es la matriz X. </span></div>
No, case is unimportant
Yes, case must match
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