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Evaluate |x y x+y y x+y xx+y x y| ....

Evaluate `|x y x+y y x+y xx+y x y|` .

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`[{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}]=[{:(2(x+y),y,x+y),(2(x+y),x+y,x),(2(x+y),x,y):}]`
`(C_(1)toC_(1)C_(2)+C_(3))`
`=2(x+)[{:(1,y,x+y),(1,x+y,x),(1+y,x,y):}]`
`=2(x+)[{:(x,-y),(x-y,-x):}]`
`=2(x+y) (-x^(2)+xy-y^(2))`
`=-2(x+y)(x^(3)-xy+y^(2))`
`=-2(x^(3)+y^(3))`
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NAGEEN PRAKASHAN ENGLISH-DETERMINANTS-Miscellaneous Exercise
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  2. Without expanding the determinant, prove that |a a^2b c bb^2c a cc^2a ...

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

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  4. " if a,b, and c are real number and " |{:(b+c,,c+a,,a+b),(c+a,,a+b,...

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  5. Solve the following determinant equation: |[x+a, b, c], [c, x+b, a],...

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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 xx+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 properties of determinants. Prove that|alphaalpha^2beta+gammarho...

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  12. For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z...

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  13. show that |{:(3a,,-a+b,,-a+c),(-b+a ,,3b,,-b+c),( -c+a,, -c+b,,3c):}| ...

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  14. Show that |(1, 1+p, 1+p+q), (2, 3+2p, 4+3p+2q), (3, 6+3p, 10+6p+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=4,4/x-6/y+5/z=1,6/x+9/y-(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. If x, y, z are non-zero real numbers, then the inverse of matrix A=[(...

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

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