Question

dada a matriz A 3x3,sendo aij= 2i+j2 calcule o determinante da matriz A. ( Me ajudem gente )

Answer 1

$A_{(3x3)}= \left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right]$

$a_{ij}=2i+j^2\\\\a_{11}=2\cdot(1)+(1)^2\\a_{11}=2+1\\a_{11}=3\\\\a_{12}=2\cdot(1)+(2)^2\\a_{12}=2+4\\a_{12}=6\\\\a_{13}=2\cdot(1)+(3)^2\\a_{13}=2+9\\a_{13}=11\\\\a_{21}=2\cdot(2)+(1)^2\\a_{21}=4+1\\a_{21}=5$

$a_{22}=2\cdot(2)+(2)^2\\a_{22}=4+4\\a_{22}=8\\\\a_{23}=2\cdot(2)+(3)^2\\a_{23}=4+9\\a_{23}=13\\\\a_{31}=2\cdot(3)+(1)^2\\a_{31}=6+1\\a_{31}=7\\\\a_{32}=2\cdot(3)+(2)^2\\a_{32}=6+4\\a_{32}=10\\\\a_{33}=2\cdot(3)+(3)^2\\a_{33}=6+9\\a_{33}=15$

$A_{3x3}= \left[\begin{array}{ccc}3&6&11\\5&8&13\\7&10&15\end{array}\right]$


$det(A)= 360+546+550-(150+390+616)\\\\det(A)=1456-1156\\\\det(A)=300$