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if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(a...

if `|{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gamma-idelta,alpha+ibeta):}|=|{:(A-iB,C-iD),(-C-iD,A+iB):}|` ,show that the producrs of sums , each of four squares , can be expressed as the sum of four squares.

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The correct Answer is:
`A=aalpha+bbeta+cgamma+ddelta,B=abeta-balpha+cdelta-dgamma,C=-agamma+bdelta+calpha-dbeta and D=adelta+bgamma-cbeta-dalpha`
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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

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  2. |{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0

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  3. if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam...

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  4. |{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" ...

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  5. Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0...

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  6. If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c...

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  7. Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b,"...

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  8. prove that , |{:(1,1+a,1+a+b),(2,3+2a,4+3a+2b),(3,6+3a,10+6a+3b):}|=1

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  9. if f(x) =|{:(sinx,cosx,tanx),(x^3,x^2,x),(2x,1,1):}| then show that li...

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  10. If 5 is one root of the equation |{:(x,3,7),(2,x,-2),(7,8,x):}|=0 then...

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  11. If y =sinpx and yn is the nth derivative of y , then find the value...

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  12. If |{:(1+ax,1+bx,1+cx),(1+a1x,1+b1x,1+c1x),(1+a2x,1+b2x,1+c2x):}|=A0+A...

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  13. Evaluate: |{:(1,1,1),(1,omega^2,omega),(1,omega,omega^2):}| (where ome...

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  14. If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lamb...

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  15. If |{:(10(c(4)),10(c(5)),11(c(m))),(11(c(6)),11(c(7)),12(c(m+2))),(12(...

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  16. If l,m and n are real numbers such that l^2+m^2+n^2=0 , then show t...

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  17. If f(x)= |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x...

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  18. If omega ne 1 is a cube root of unity , then find the value of |{:(...

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  19. If alpha is a cube root of unity , then find the value of |{:(alpha...

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  20. If f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha)...

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