Página — Matematica 9° Secundaria (pág. 51)

Después de organizar las constantes, comenzaremos con el desarrollo de los determinantes menores del primer renglón para evaluar a |\mathsf{A}|,|\mathsf{A}_{_x}|,|\mathsf{A}_{_y}|,|\mathsf{A}_{_z}|

\left|\boldsymbol{A}\right|=\left|\begin{array}{ccc}3&-2&-1\\2&3&-2\\1&-4&1\\\end{array}\right|=3\left|\begin{array}{cc}3&-2\\-4&1\\\end{array}\right|-2\left|\begin{array}{cc}-2&-1\\-4&1\\\end{array}\right|+1\left|\begin{array}{cc}-2&-1\\3&-2\\\end{array}\right|

|A|=3[(3)(1)-(-4)(-2)]-2[(-2)(1)-(-4)(-1)]+1[(-2)(-2)(3)(-1)]

\left|\mathrm{A}\right|=3\left[3-8\right]-2\left[-2-4\right]+1\left[4+3\right]

|A|=3(-5)-2(-6)+1(7)

|A|=-15+12+7

|A|=4

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{matrix}-6&-2&-1\\ 1&3&-2\\ -3&-4&-1\end{matrix}\right|=-6\left|\begin{matrix}3&-2\\ -4&1\end{matrix}\right|-1\left|\begin{matrix}-2&-1\\ -4&1\end{matrix}\right|+(-3)\left|\begin{matrix}-2&-1\\ 3&-2\end{matrix}\right|

|A|=-6[(3)(1)-(-4)(-2)]-1[(-2)(1)-(-4)(-1)]+(-3)[(-2)(-2)-(3)(-1)]

|A_{x}|=-6[3-8]-1[-2-4]-3[4+3]

|A_{x}|=-6(-5)-1(-6)-3(-7)

|A_{x}|=30+6-21

|A_{x}|=15

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

\left|\mathsf{A}_{y}\right|=\left|\begin{array}{ccc}3&-6&-1\\2&1&-2\\1&-3&1\\\end{array}\right|=3\left|\begin{array}{cc}1&-2\\-3&1\\\end{array}\right|-2\left|\begin{array}{cc}-6&-1\\-3&1\\\end{array}\right|+1\left|\begin{array}{cc}-6&-1\\1&-2\\\end{array}\right|

Matemáticas•Grado 9

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