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Show that: |(a, b-c,c+b), (a+c, b, c-a),...

Show that: `|(a, b-c,c+b), (a+c, b, c-a), (a-b,b+a, c)|=(a+b+c)(a^2+b^2+c^2)dot`

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To show that the determinant \[ \begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & b+a & c \end{vmatrix} ...
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Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)+c^(2)) .

Prove that |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=(a+b+c)(a^2+b^2+c^2)

Prove that: |(a,a+c,a-b),(b-c,b,b+a),(c+b,c-a,c)|=(a+b+c)(a^(2)+b^(2)+c^(2))

det[[ Show that a,b-c,c+ba+c,b,c-aa-b,b+a,c]]=(a+b+c)(a^(2)+b^(2)+c^(2))

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

Show that |((b+c)^2,a^2,bc),((c+a)^2,b^2,ca),((a+b)^2,c^2,ab)|=(a^2+b^2+c^2)(a+b+c)(a-b)(b-c)(c-a).

Prove that |[a+b+c, -c, -b],[-c, a+b+c, -a],[-b, -a, a+b+c]|=2(a+b)(b+c)(c+a)

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

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Find a quadratic polynomial phi(x) whose zeros are the maximum and mi...

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  2. Let f(x)=|secxcosxsec^2x+cotxcos e cxcos^2xcos^2x cos e c^2x1cos^2xcos...

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  3. Show that: |(a, b-c,c+b), (a+c, b, c-a), (a-b,b+a, c)|=(a+b+c)(a^2+b^2...

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  4. If a , b , c are real numbers, prove that |a b c b c a c a b|=-(a+b+c)...

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  5. Solve: |(a+x, a-x, a-x),(a-x, a+x, a-x),(a-x, a-x, a+x)|=0

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  6. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

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  7. 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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  8. Solve : |(x-2, 2x-3, 3x-4), (x-4, 2x-9, 3x-16) ,(x-8 ,2x-27,3x-64)|=0

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  9. If x+y+z=0 , prove that |[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y ...

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  10. If a , b , c are all positive and are p t h ,q t ha n dr t h terms of ...

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  11. Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-...

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  12. |[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]|...

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  13. Prove that : |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|...

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  14. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

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  15. Prove that: |[a, b, ax+by],[ b, c, bx+cy], [ax+by, bx+cy,0]|=(b^2-a c)...

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  16. Without expanding the determinant, show that (a+b+c) is a factor of th...

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  17. If m in N and mgeq2, prove that: |1 1 1m(C1)m+1(C1)m+2(C1)m(C2)m+1(C2...

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  18. Evaluate: =|10 ! 11 ! 12 ! 11 ! 12 ! 13 ! 12 ! 13 ! 14 !|

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  19. Show that: |b+cc+a a+b q+r r+p p+q y+z z+xx+y|=2|a b c p q r x y z|

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  20. Prove that |(1+a,1, 1),( 1,a+b,1),( 1, 1, 1+c)|=a b c(a+1/a+1/b+1/c)=a...

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