[" If "A=[[a,c,b],[b,a,c],[c,b,a]]" then the cofactor of "a_(3)" in "],[" A "+A^(T)" is "],[[" 1) "-(2a(b+c)-(b+c)^(2))," 2) "ac-b^(2)],[" 3) "a^(2)-bc," 4) "2a(a+c)-(a+c)^(2)]]

(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ac)

Prove that Delta = |{:(1,,1,,1),(a,,b,,c),(bc+a^(2),,ac+b^(2),,ab+c^(2)):}| = 2(a-b)(b-c)(c-a)

If a,b, and c are in H.P.then th value of ((ac+ab-bc)(ab+bc-ac))/((abc)^(2)) is ((a+c)(3a-c))/(4a^(2)c^(2)) b.(2)/(bc)-(1)/(b^(2)) c.(2)/(bc)-(1)/(a^(2)) d.((a-c)(3a+c))/(4a^(2)c^(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:

(1)/(c),(1)/(c),-(a+b)/(c^(2))-(b+c)/(c^(2)),(1)/(a),(1)/(a)(-b(b+c))/(a^(2)c),(a+2b+c)/(ac),(-b(a+b))/(ac^(2))]| is

If A = [[0,c,-b],[-c,0,a],[b,-a,0]] and B = [[a^(2),ab,ac],[ab,b^2,bc],[ac,bc,c^(2)]] then A B=

If A=[[0 ,c,-b],[-c, 0, a],[ b, -a, 0]] and B=[[a^2, ab, ac],[ ab, b^2 , bc],[ ac ,bc, c^2]] , show that A B=B A=O_3xx3 .

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =5 , then the value of Delta = |(b_(2) c_(3) - b_(3) c_(2),a_(3) c_(2) - a_(2) c_(3),a_(2) b_(3) -a_(3) b_(2)),(b_(3) c_(1) - b_(1) c_(3),a_(1) c_(3) - a_(3) c_(1),a_(3) b_(1) - a_(1) b_(3)),(b_(1) c_(2) - b_(2) c_(1),a_(2) c_(1) - a_(1) c_(2),a_(1) b_(2) - a_(2) b_(1))| is