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Using properties of determinants, prove the following `|(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2`.

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Using properties of determinants, prove the following |(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

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By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  2. If a1,a2,a3,.....an.... are in G.P. then the determinant 'Delta=|[loga...

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  3. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

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  4. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

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  5. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

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  6. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

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  7. If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, the...

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  8. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

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  9. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

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  10. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

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  11. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

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  12. 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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  13. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...

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  14. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

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  15. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

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  16. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

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  17. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

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  18. If Dk=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum(k=1)^n Dk=56. then n eq...

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  19. If a!=p ,b!=q ,c!=r and |[p, b, c ],[a, q, c ],[a ,b, r]|=0, then find...

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  20. If x1,x2,x3 as well as y1, y2, y3 are in G.P. with same common rati...

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