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Find the coordinates of the centriod of ...

Find the coordinates of the centriod of the triangle whose vertices are `( a_(1), b_(1), c_(1)) , (a_(2), b_(2), c_(2))` and `(a_(3), b_(3), c_(3))`.

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if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if A_(1) ,B_(1),C_(1) ……. are respectively the cofactors of the elements a_(1) ,b_(1),c_(1)…… of the determinant Delta = |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}|, Delta ne 0 then the value of |{:(B_(2),,C_(2)),(B_(3),,C_(3)):}| is equal to

if A_(1) ,B_(1),C_(1) ……. are respectively the cofactors of the elements a_(1) ,b_(1),c_(1)…… of the determinant Delta = |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}|, Delta ne 0 then the value of |{:(B_(2),,C_(2)),(B_(3),,C_(3)):}| is equal to

If (b_(2)-b_(1))(b_(3)-b_(1))+(a_(2)-a_(1))(a_(3)-a_(1))=0 then plove that the circumcenter of the triangle having vertices (a_(1),b_(1)),(a_(2),b_(2)) and (a_(3),b_(3)) is ((a_(2+a_(3)))/(2),(b_(2+)b_(3))/(2))

Let A= |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3)c_(3))| then the cofactor of a_(31) is:

In algebra, the determinant is useful value that can be computer from the elements of a square matrix. The determinant is represented as det 'A' or |A| and its value can be evaluated by the expansion of the determinant as given below (A) Expansion of two order determinant : (B) Expansion of 3^(rd) order determinant (i) With respect to first fow : |A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=a_(1)|{:(b_(2),c_(2)),(b_(3),c_(3)):}|-b_(1)|{:(a_(2),c_(2)),(a_(3),c_(3)):}|+c_(1)|{:(a_(2),b_(2)),(a_(3),b_(3)):}| =a_(1)(b_(2)c_(3)-b_(3)c_(2))-b_(1)(a_(2)c_(3)-a_(3)c_(2))+c_(1)(a_(2)b_(3)-b_(2)a_(3)) (ii) With respect to second column : |A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=-b_(1)|{:(a_(2),c_(1)),(a_(3),c_(3)):}|+b_(2)|{:(a_(1),c_(1)),(a_(3),c_(3)):}|-b_(3)|{:(a_(1),c_(1)),(a_(2),c_(2)):}| Similarly a determinant can be expanded with respect to any row or column The value of k for which determinant |{:(2,3,-1),(-1,-2,k),(1,-4,1):}| vanishes, is "(a) -3 (b) 7/11 (c) -2 (d) 2"

In algebra, the determinant is useful value that can be computer from the elements of a square matrix. The determinant is represented as det 'A' or |A| and its value can be evaluated by the expansion of the determinant as given below (A) Expansion of two order determinant : (B) Expansion of 3^(rd) order determinant (i) With respect to first fow : |A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=a_(1)|{:(b_(2),c_(2)),(b_(3),c_(3)):}|-b_(1)|{:(a_(2),c_(2)),(a_(3),c_(3)):}|+c_(1)|{:(a_(2),b_(2)),(a_(3),b_(3)):}| =a_(1)(b_(2)c_(3)-b_(3)c_(2))-b_(1)(a_(2)c_(3)-a_(3)c_(2))+c_(1)(a_(2)b_(3)-b_(2)a_(3)) (ii) With respect to second column : |A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=-b_(1)|{:(a_(2),c_(1)),(a_(3),c_(3)):}|+b_(2)|{:(a_(1),c_(1)),(a_(3),c_(3)):}|-b_(3)|{:(a_(1),c_(1)),(a_(2),c_(2)):}| Similarly a determinant can be expanded with respect to any row or column The value of the determinant |{:(2,3,4),(6,5,7),(1,-3,2):}|is: "(a) 54 (b) 40 (c) -45 (d) -40"

In algebra, the determinant is useful value that can be computer from the elements of a square matrix. The determinant is represented as det 'A' or |A| and its value can be evaluated by the expansion of the determinant as given below (A) Expansion of two order determinant : (B) Expansion of 3^(rd) order determinant (i) With respect to first fow : |A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=a_(1)|{:(b_(2),c_(2)),(b_(3),c_(3)):}|-b_(1)|{:(a_(2),c_(2)),(a_(3),c_(3)):}|+c_(1)|{:(a_(2),b_(2)),(a_(3),b_(3)):}| =a_(1)(b_(2)c_(3)-b_(3)c_(2))-b_(1)(a_(2)c_(3)-a_(3)c_(2))+c_(1)(a_(2)b_(3)-b_(2)a_(3)) (ii) With respect to second column : |A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=-b_(1)|{:(a_(2),c_(1)),(a_(3),c_(3)):}|+b_(2)|{:(a_(1),c_(1)),(a_(3),c_(3)):}|-b_(3)|{:(a_(1),c_(1)),(a_(2),c_(2)):}| Similarly a determinant can be expanded with respect to any row or column. The vaue of the determinant |{:(5,1),(3,2):}|is: "(a) 4 (b) 5 (c) 6 (d) 7 "