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Show that |(1, 1+p, 1+p+q), (2, 3+2p, 4+...

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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`L.H.S.=|{:(1,1+p,1+p+q),(2,3+p,4+3p+2q),(3,6+3p,10+6p+3q):}|=|{:(1,1+p,1+p+q),(0,1,2+p),(0,3,7+3p):}|`
`(R_(2)toR_(2)-3R_(1),R_(3)toR_(3)-3R_(1))`
`=1|{:(1,2+p),(3,7+3p):}|=(7+3p)-3(2+p)`
=1=R.H.S.
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NAGEEN PRAKASHAN ENGLISH-DETERMINANTS-Miscellaneous Exercise
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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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  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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  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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