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Using the property of determinants and without expanding, prove that:`|[b+c, q+r, y+z],[ c+a, r+p, z+x],[ a+b, p+q, x+y]|=2|[a, p, x],[ b, q ,y],[ c, r, z]|`

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To prove that \[ |[b+c, q+r, y+z],[ c+a, r+p, z+x],[ a+b, p+q, x+y]|=2|[a, p, x],[ b, q ,y],[ c, r, z]| \] we will use properties of determinants without expanding them. ...
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Using the property of determinants and without expanding, prove that:...

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  2. Using the property of determinants and without expanding, prove that:...

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  3. Using the property of determinants and without expanding, prove that:...

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  4. Using the property of determinants and without expanding, prove that:...

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  5. Using the property of determinants and without expanding, prove that:...

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  6. Using the property of determinants and without expanding, prove that:...

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  7. Using the property of determinants and without expanding, prove that:...

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  8. By using properties of determinants. Show that:|[x,x^2,y z],[ y, y^2,z...

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  9. By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,...

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  10. If a, b, c are positive and unequal, show that value of the determina...

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  11. If a,b,c are in A.P, find value of |[2y+4,5y+7,8y+a],[3y+5,6y+8,9y+b],...

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  12. Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2x y...

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  13. Use product [1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2] to solve th...

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  14. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

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  15. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x...

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  16. By using properties of determinants. Show that: (i) |[a-b-c,2a,2a],[2b...

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  17. By using properties of determinants. Show that:|[1,x,x^2],[x^2, 1,x],[...

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  18. By using properties of determinants. Show that:|[1+a^2-b^2, 2a b,-2b],...

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

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  20. Let A be a square matrix of order 3xx3, then |k A|is equal to (A) k|A...

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