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prove that |{:((a-x)^(2),,(a-y)^(2),,(a-...

prove that `|{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),,(b-z)^(2)),((c-x)^(2),,(c-y)^(2),,(c-z)^(2)):}|`
`|{:((1+ax)^(2),,(1+bx)^(2),,(1+cx)^(2)),((1+ay)^(2),,(1+by)^(2),,(1+cy)^(2)),((1+az)^(2),,(1+bx)^(2),,(1+cz)^(2)):}|`
`=2 (b-c)(c-a)(a-b)xx (y-z) (z-x)(x-y)`

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RESONANCE-MATRICES & DETERMINANT-HLP
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  2. prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...

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  3. Prove that Delta=|{:(,beta(gamma),beta(gamma)'+beta'(gamma),beta'(gamm...

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  4. If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...

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  5. if (x(1),x(2))^(2)+(y(1)-y(2))^(2)=a^(2), (x(2)-x(3))^(2)+(y(2)-y(3))^...

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  6. Let A=[(cos^(- 1)x,cos^(- 1)y,cos^(- 1)z),(cos^(- 1)y,cos^(- 1)z,cos^...

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  7. If y=(u)/(v), where u and v are functions of x, show that v^(3)(d^(2...

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  8. If alpha&beta be the real roots of ax^(2)+bx+c=0 and s(n)=alpha^(n)+be...

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  9. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

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  10. Let overset(to)(a(r))=x(r )hat(i)+y(r )hat(j)+z(r )hat(k),r=1,2,3 thre...

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  11. If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3)...

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  12. If the determinant |(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h)| splits ...

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  13. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

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  14. If a,b,c are comples number and z=|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c...

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  15. If f(x)=log(10)x and g(x)=e^(ln x) and h(x)=f [g(x)], then find the va...

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  16. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

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  17. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

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  18. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

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  19. Let 'A' is (4xx4) matrix such that the sum of elements in each row is ...

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  20. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

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