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Evaluate abs[{:(cosalphacosbeta,cosalp...

Evaluate
`abs[{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}]`

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`[{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}]`
`=cosalphacosbeta(cosalphacosbeta-0)-cosalphasinbeta(-sinbetacosalpha-0)-sinalpha(-sin^(2)betasinalpha-sinalphacos^(2)beta)`
`=cos^(2)alpha(cos^(2)beta+sin^(2)beta)+sin^(2)alpha`
`=cos^(2)alpha+sin^(2)=1`
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NAGEEN PRAKASHAN-DETERMINANTS-Miscellaneous Exercise
  1. Prove that the determinant [xsinthetacostheta-sintheta-x1costheta1x]is...

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  2. Show without expanding at any stage that: [a,a^2,bc],[b,b^2,ca],[c,c^...

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  3. Evaluate abs[{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta...

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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, b,c],[a,x+b,c],[a,b,x+c]|=0

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  6. Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^...

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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. Prove that [[x, x^2 , 1+px^3], [y, y^2, 1+py^3] ,[z, z^2, 1+pz^3]] = (...

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  13. Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

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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. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

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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=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

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