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Simply |{:(,a,b,c),(,a^(2),b^(2),c^(2)),...

Simply `|{:(,a,b,c),(,a^(2),b^(2),c^(2)),(,bc,ca,ab):}|`

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Given determinant is equal to
`=(1)/(abc)|{:(,a^(2),b^(2),c^(2)),(,a^(3),b^(3),c^(3)),(,abc,abc,abc):}|=|{:(,a^(2),b^(2),c^(2)),(,a^(3),b^(3),c^(3)),(,1,1,1):}|`
Apply `C_(1)toC_(1)-C_(2), C_(2)toC_(2)-C_(3)`
`|{:(,a^(2)-b^(2),b^(2)-c^(2),c^(2)),(,a^(3)-b^(3),b^(3)-c^(3),c^(3)),(,0,0,1):}|`
`(a-b)(b-c) [ab^(2)+abc+ac^(2)+b^(3)+b^(2)C+bc^(2)-a^(2)b=a^(2)c-ab^(2)-abc-b^(3)-b^(2)c`
`=(a-b)(b-c)[c(ab+bc+ca)-a(ab+bc+ca)]`
`=(a-b)(b-c)(c-a)(ab+bc+ca)`
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Without expanding determinant at any stage evaluate |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|

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Let a, b and c are the roots of the equation x^(3)-7x^(2)+9x-13=0 and A and B are two matrices given by A=[(a,b,c),(b,c,a),(c,a,b)] and B=[(bc-a^(2),ca-b^(2),ab-c^(2)),(ca-b^(2),ab-c^(2),bc-a^(2)),(ab-c^(2),bc-a^(2),ca-b^(2))] , then the value |A||B| is equal to

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

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RESONANCE ENGLISH-MATRICES & DETERMINANT-HLP
  1. Simply |{:(,a,b,c),(,a^(2),b^(2),c^(2)),(,bc,ca,ab):}|

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  2. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

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  3. 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(...

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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 are the roots of the equation ax^(2)+bx+c=0 and S(n)=al...

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  9. Let a >0,d >-0. Find the value of the determinant |1/a1/(a(a+d))1/((a+...

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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. about to only mathematics

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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,b,c are real number, and D=|{:(,a,1+2i,3-5i),(,1-2i,b,-7-3i),(,3+...

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

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

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

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  20. Let A be a (4xx4) matrix such that the sum of elements in each row is ...

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

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