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Using properties of determinants, prove the following: `|3"a"-"a"+"b"-"a"+"c""a"-"b"3"b""c"-"b""a"-"c""b"-"c"3"c"|=3("a"+"b"+"c")("a b"+"b c"+"c a")`

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MODERN PUBLICATION-DETERMINANTS-Miscellaneous Exercise on Chapter 4
  1. Prove that the determinant |{:(x,sintheta,costheta),(-sintheta,-x,1),(...

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  2. Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b...

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  3. Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,co...

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  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

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  5. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  6. Prove that |a^2b c a c+c^2a^2+a bb^2a c a bb^2+b cc^2|=4a^2b^2c^2 .

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  7. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  8. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}]. Verify that ltbtgt (i) [adjA]^...

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  9. Evaluate: [[x,y,x+y],[y,x+y,x],[x+y,x,y]]

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  10. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

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  11. Using peoperties of determinants in questions 11 to 15, prove that : ...

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  12. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  13. Using properties of determinants, prove the following: |3"a"-"a"+"...

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  14. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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  15. Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, ...

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  16. 2/x+3/y+10/z=4, 4/x-6/y+5/z=1, 6/x+9/y-20/z=2

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  17. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

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  18. Choose the correct answer in questions 17 to 19: If x, y, z are non...

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  19. Let A=[(1,sintheta, 1),(-sintheta, 1, sintheta),(-1, -sintheta, 1)], w...

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