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Show that in general there are three values of t for which the following system of equations has a non- trival solution (a-t)x+by+cz=0, bx+(c-t)y+az=0 and cx+ay+(b-t)z=0.
Express the product of these values of t in the form of a determinant.

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The correct Answer is:
`|{:(a,b,c),(b,c,a),(c,a,b):}|`
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ARIHANT MATHS-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 that: |[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 determinat |{:(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(...

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  4. The value of the determinant |(bc,ca,ab),(p,q,r),(1,1,1)|, where a, b ...

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  5. Whitout expanding the determinat 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. If A,B and C are the angles of a triangle and |{:(1,1,1),(1+sinA,1+si...

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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 and v are functions of x, show that v^(3)(d^(2...

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

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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. prove that |(1/(a-a1)^2,1/(a-a1),1/a1),(1/(a-a2)^2,1/(a-a2),1/a2),(1/...

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

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  16. Eliminates (i) a,b, and c (ii) x,y,z from the equations -a+(by)...

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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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