Without expanding, show that the value of the following determinant is zero: `|[49, 1, 6], [39, 7, 4], [26, 2, 3]|`

Without expanding, show that the value of each of the following determinants is zero: |1^2 2^2 3^2 4^2\ \ \ 2^2 3^2 4^2 5^2\ \ \ 3^2 4^2 5^2 6^2\ \ \ 4^2 5^2 6^2 7^2| (ii) |a b c a+2x b+2y c+2z x y z| (iii) |(2^x+2^(-x))^2(2^x-2^(-x))^2 1(3^x+3^(-x))^2(3^x-3^(-x))^2 1(4^x+4^(-x))^2(4^x-4^(-x))^2 1|

Write the value of the following determinant: |[102, 18, 36],[ 1, 3, 4],[17, 3, 6]|

Write the value of the following determinant: |[102, 18, 36],[ 1, 3, 4],[17, 3, 6]|

Find the values of the following determinants |{:(3,4),(1,2):}|

Without expanding, show that the value of each of the following determinant is zero: \begin{vmatrix} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \\ \end{vmatrix}

Without expanding, show that the value of each of the following determinants is zero: |1//a , a^2b c1//bb^2a c1//cc^2a b| (ii) |a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b| (iii) |1a a^2 1bb^2 1cc^2\ \ \ -b c-a c-a b|

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding, show that the value of the following determinant is zero: |[sinalpha,cosalpha,cos(a+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]|

Without expanding at any stage, prove that the value of each of the following determinants is zero. (1) |[0,p-q,p-r],[q-p,0,q-r],[r-p,r-q,0]| (2) |[41,1,5],[79,7,9],[29,5,3]| (3) |[1,w,w^2],[w,w^2,1],[w^2,1,w]| , where w is cube root of unity

Without expanding, show that the value of each of the determinants is zero: |1/a a^2 bc 1/b b^2 ac 1/c c^2 ab|