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Show that: |[a, a+b ,a+b+c],[2a,3a+2b,4a...

Show that: `|[a, a+b ,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]|=a^3` .

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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

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)

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

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) .

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)dot

If a!=6,b,c satisfy |[a,2b,2c],[3,b,c],[4,a,b]|=0 ,then abc =

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

Add : a - 3b + 3, 2a + 5 - 3c, 6c - 15 + 6b

Add : 6- 3a + b , a - 7-6b and 3b + 2- a.

Add : 5a+6b-3c, 4b+c-3a and a-6c-3b .

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Prove that: |x+yx x5x+4y4x2x 10 x+8y8x3x|=x^3 .

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  2. Show that: |[1 ,1+p,1+p+q],[2, 3+2p,1+3p+2q],[3, 6+3p,1+6p+3q]|=1 .

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  3. Show that: |[a, a+b ,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]...

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  4. Show that: |[b+c,c+a ,a+b],[ q+r, r+p, p+q],[ y+z ,z+x,x+y]|=2|[a, b, ...

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  5. Prove that: determinant \begin{vmatrix} 1+ a & 1 & 1 \\ 1 & 1+b...

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  6. If a ,\ b ,\ c are the roots of the equation x^3+p x+q=0 , then find...

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  7. Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^3

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  8. 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)...

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  9. Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^...

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  10. 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...

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  11. Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2...

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

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  13. If a ,\ b ,\ c are roots of the equation x^3+p x+q=0 , prove that d...

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  14. Find dy/dx if y=cos^2x

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  15. If a+b+c!=0 and , \begin{vmatrix} a & b & c \\ b & c & a \\ ...

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

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

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

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

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