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Show that: |a b-cc+b a+c b c-a a-bb+a c|...

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

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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

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) .

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)

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2\ b^2\ c^2 .

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

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

Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

Using the property of determinants and without expanding, prove that: |-a^2a b a c b a b^2b cc a c b-c^2|=4a^2b^2c^2

If each of a, b and c is a non-zero number and (a)/(b)= (b)/(c ) , show that: (a + b+c) (a-b + c) = a^(2) + b^(2) + c^(2)

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If a+b+c!=0 and , \begin{vmatrix} a & b & c \\ b & c & a \\ ...

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  2. If a , b , c are real numbers, prove that \begin{vmatrix} a & b & ...

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

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  4. Using properties of determinants. Prove that |[3a,-a+b,-a+c], [-b+a,3b...

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  5. Using properties of determinants, solve for x:|[a+x, a-x, a-x], [a-x...

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  6. Using properties of determinants, solve the following for x: |[x-2,...

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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. If a , b , c are all positive and are p t h ,q th and r t h terms of a...

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  9. If x+y+z=0 prove that | xa yb zc yc za xb zb xc ya y|=x y z|a b c...

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  10. Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a ...

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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. Find a quadratic polynomial varphi(x) whose zeros are the maximum ...

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  13. f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,...

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  14. Let "T"r=|[r ,x,(n(n+1))/2], [2r-1,y, n^2],[ 3r-2,z,(n(3n-1))/2]| .whe...

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  15. If "Delta"r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, ...

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  16. If m is a positive integer and Dr=|(2r-1,\ ^m Cr,1),(m^2-1, 2^m ,m+1...

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  17. Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b,...

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  18. Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x...

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  19. Prove that: |(-2a , a+b, a+c),( b+a,-2b, b+c),( c+a , c+b,-2c)|=4(a+b...

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  20. Evaluate the following determinant: |[1 ,3, 5], [2 ,6, 10], [31, 11,...

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