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If x, y, z are not all zero & if ax + ...

If `x, y, z` are not all zero & if `ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0`, then prove that `x: y : z = 1 : 1 : 1` OR `1 :omega:omega^2 OR 1:omega^2:omega` , where `omega` is one ofthe complex cube root of unity.

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ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Subjective Type Questions)
  1. Prove that |{:(b+c,c,b),(c,c+a,a),(b,a,a+b):}| = 4 abc

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  2. Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  3. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

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  4. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

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  5. Without expanding the determinant at any stage prove that |{:(-5,3+5i...

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  6. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

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  7. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

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  8. The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaal...

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  9. If y=(u)/(v), where u & v are functions of 'x' show that v^(3)(d^(2)y)...

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  10. Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+al...

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  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

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  12. (i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin...

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  13. If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| t...

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  14. If |A| = 2 and A = | (2x, 6) , (5x, 1)| then find the value of x

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  15. Show that in general there are three values of t for which the followi...

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  16. Find dy/dx if y=13x-y^2

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  17. If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx ...

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