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Show that: |b+c c+a a+b q+r r+p p+q y+z ...

Show that: `|b+c c+a a+b q+r r+p p+q y+z z+x x+y|=2|a b c p q r x y z|`

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To show that \[ \begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix} ...
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Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

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Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r q x+r y p x+q y q x+r y0| is- a. zero b. positive c. negative \ d. q^2+p r

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]|

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. 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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  2. Evaluate: =|(10 !, 11 !, 12 !), (11 !, 12 !, 13 !), (12 !, 13 !, 14 !)...

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

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  4. Prove that |[1+a,1, 1], [1,1+b,1], [1, 1, 1+c]|=a b c(1+1/a+1/b+1/c)=a...

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  5. If a , b , c , are roots of the equation x^3+p x+q=0, prove that |[a...

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  6. If a+b+c!=0 and |a b c b c a c a b|=0 , then prove that a=b=cdot

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  7. Let a , band c detnote the sides BC,CA andAB respectively of triangl...

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  8. Prove that |[a^2+2a,2a+1,1],[2a+1,a+2,1],[3,3,1]|=(a-1)^3

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  9. Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca...

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  10. Using properties of determinants, show that triangle ABC is isosceles,...

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  11. In a triangleABC, if |[1,1,1][1+sinA,1+sinB,1+sinC],[sinA+sin^2A, sinB...

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  12. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

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  13. Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0...

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  14. If A is a skew-symmetric matrix of odd order n , then |A|=0

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  15. Using properties of determinants, show that |{:(x, p, q), ( p, x, q)...

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  16. If f(x)=|[a,-1 ,0],[ax,a,-1],[a x^2,a x, a]|, using properties of det...

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  17. If a , b , c are distinct real numbers and the system of equations a x...

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  18. If x , y , z are not all zero such that a x+y+z=0, x+b y+z=0, ...

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  19. Find the value of lambda for which the homogeneous system of equations...

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  20. If the system of equations x=c y+b z y=a z+c x z=b x+a y has...

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