Página — Matematica 9° Secundaria (pág. 49)

Reemplazamos de acuerdo a \left|\mathsf{A}_{\mathsf{x}}\right|=\left|\begin{matrix}d_{_1}&b_{_1}&c_{_1}\\ d_{_2}&b_{_2}&c_{_2}\\ d_{_3}&b_{_3}&c_{_3}\end{matrix}\right|\mathsf{y} 'desarrollamos

\left|\boldsymbol{A}_{x}\right|=\left|\begin{array}{ccc}-6&4&-3\\12&-8&5\\-3&4&-2\\\end{array}\right|=-6\left|\begin{array}{cc}-8&5\\4&-2\\\end{array}\right|-12\left|\begin{array}{cc}4&-3\\4&-2\\\end{array}\right|-3\left|\begin{array}{cc}4&-3\\-8&5\\\end{array}\right|

|A|=-6[(-8)(-2)-(4)(5)]-12[(4)(-2)-(4)(-3)]-3[(4)(5)-(-8)(-3)]

|A|=-6[16-20]-2[-8+12]-3[20-24]

|A_{x}|=-6(-4)-12(4)-3(-4)

\left|A_{x}\right|=24-48+12

|A_{x}|=-12

Reemplazamos de acuerdo a \left|\mathsf{A}_{y}\right|=\left|\begin{matrix}a_{_1}&d_{_1}&c_{_1}\\ a_{_2}&d_{_2}&c_{_2}\\ a_{_3}&d_{_3}&c_{_3}\end{matrix}\right|\mathsf{y} 'desarrollamos

\begin{aligned}&|\mathsf{A}_{y}|=\left|\begin{array}{ccc}1&-6&-3\\2&12&5\\3&-3&-2\\\end{array}\right|=1\left|\begin{array}{cc}12&5\\-3&-2\\\end{array}\right|\left.-2\left|\begin{array}{cc}-6&-3\\-3&-2\\\end{array}\right|+3\left|\begin{array}{cc}-6&-3\\12&5\\\end{array}\right|\right.\\ &|\mathsf{A}_{y}|=1\left[(12)(-2)(-3)(5)\right]-2\left[(-6)(-2)(-3)(-3)\right]+3\left[(-6)(5)(-(12)(-3))\right]\\ &|\mathsf{A}_{y}|=1\left[-24+15\right]-2\left[12-9\right]+3\left[-30+36\right]\\ &|\mathsf{A}_{y}|=1\left(-9\right)-2(3)+3(6)\\ &|\mathsf{A}_{y}|=-9-6+18\\ &|\mathsf{A}_{y}|=3\\ \end{aligned}

Por último, reemplazamos de acuerdo a \left|\mathsf{A}_{z}\right|=\left|\begin{matrix}a_{_1}&b_{_1}&d_{_1}\\ a_{_2}&b_{_2}&d_{_2}\\ a_{_3}&b_{_3}&d_{_3}\end{matrix}\right|\mathsf{y} /desarrollamos

Matemáticas· Grado 9

48