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Using properties of determinants. Prove ...

Using properties of determinants. Prove that`|[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a)`

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To prove that \[ |[3a, -a+b, -a+c], [-b+a, 3b, -b+c], [-c+a, -c+b, 3c]| = 3(a+b+c)(ab+bc+ca) \] we will use properties of determinants. Let's denote the determinant as \( D \). ...
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Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a) .

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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)

Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca] , [1 , c , a b]|=(a-b)(b-c)(c-a)

Using properties of determinants, prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]|=a^3

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Using properties of determinants, prove the following : |[a, a^2,bc],[b,b^2,ca],[c,c^2,ab]|=(a-b)(b-c)(c-a)(b c+c a+a b)

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Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a+b+c|=2(a+b)(b+c)(c+a)

NCERT ENGLISH-DETERMINANTS-All Questions
  1. Using properties of determinants. Prove that |(sinalpha,cosalpha,cos(a...

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  2. Using properties of determinants. Prove that|[1 ,1+p,1+p+q],[2, 3+2p,4...

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

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  4. Using properties of determinants, prove the following: |xx^2 1+p x...

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  5. Using properties of determinants. Prove that|(alpha,alpha^2,beta+gamma...

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  6. Evaluate |[1,x, y],[1,x+y, y],[1,x,x+y]|

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  7. Write Minors and Cofactors of the elements of following determinants:...

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  8. Using Cofactors of elements of second row, evaluate Delta=|(5, 3, 8),(...

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  9. Write Minors and Cofactors of the elements of following determinants:...

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  10. If Delta=|[a(11),a(12),a(13)],[a(21),a(22),a(23)],[a(31),a(32),a(33)]|...

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  11. Using Cofactors of elements of third column, evaluate Delta=|(1,x, y ...

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  12. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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  13. EvaluateDelta=|1a b c1b c a1c a b|

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  14. Show that |a b c a+2x b+2y c+2z x y z|=0

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  15. Prove that |a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3

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  16. Show that|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc(1+1/a+1/b+1/c)=abc+bc+ca+...

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  17. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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  18. Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

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  19. If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=...

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  20. Find the equation of the line joining A( 1,3) and B (0,0) using deter...

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