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|(a, a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c...

`|(a, a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0, |(a, a^(2),1),(b,b^(2),1),(c,c^(2),1)|!=0`అయితే abc=-1 అని చూపండి.

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`abc=-1`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -TEXTUAL EXERCISES (EXERCISE -3( d)
  1. |(a,b,c),(b,c,a),(c,a,b)|=

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  2. Find the determinant of the matrix [(1^(2),2^(2),3^(2)),(2^(2),3^(2),4...

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  3. IF A=[{:(1,0,0),(2,3,4),(5,-6,x):}] and det A=45 then find x.

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  4. Show that |{:(bc,b+c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)

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  5. |(b+c, c+a, a+b),(a+b, b+c, c+a),(a, b,c)]=a^(3)+b^(3)+c^(3)-3abcఅని చ...

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  6. Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz

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  7. |(a, a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0, |(a, a^(2)...

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  8. Without expanding the determinant, prove that: (i) |{:(alpha, alpha^...

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  9. Without expanding the determinant, prove that: |{:(alpha xi, beta psi...

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  10. Without expanding the determinant, prove that: |{:(1, beta gamma, be...

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  11. If Delta(1)=|{:(a(1)^(2)+b(1)+c(1),a(1)a(2)|b(2)|c(2),a(1)a(3)+b(3)+c(...

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  12. Delta1=|(1,cos alpha, cos beta),(cos alpha , 1, cos gamma),(cos beta, ...

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  13. Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

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  14. Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(...

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  15. Show that |{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3

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  16. Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-...

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  17. Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...

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  18. Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

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  19. Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

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  20. Show that |{:(x,a,a),(a,x,a),(a,a,x):}|=(x+2a)(x-a)^2

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