Prove: `|b+c a a b c+a b cc a+b|=4a b c`

Prove that |b+c a a b c+a b cc a+b|=4a b c

Prove that |b+c a a b c+a b c c a+b |

Using the property of determinants and without expanding, prove that: |-a^2a b a c b a b^2b cc a c b-c^2|=4a^2b^2c^2

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is |a-c-b-c b-a-b-a c| (b) |a b c b c a c a b| |a c bb a cc b a| (d) |a a+bb+c bb+cc+a cc+a a+b|

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is |a-c-b-c b-a-b-a c| (b) |a b c b c a c a b| |a c bb a cc b a| (d) |a a+bb+c bb+cc+a cc+a a+b|

Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

Prove that =|a cc-a a+cc bb-c b+c a-bb-c0a-c x y z1+x+y|=0 implies that a ,b ,c are in A.P. or a ,c ,b are in G.P.

Prove that |b c-a^2c a-b^2a b-c^2-b c+c a+a bb c-c a+a bb c+c a-a b(a+b)(a+c)(b+c)(b+a)(c+a)(c+b)|=3.(b-c)(c-a)(a-b)(a+b+c)(a b+b c+c a)

Prove the identities: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2b^2c^2

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2\ b^2\ c^2 .