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Solve the following determinant equati...

Solve the following determinant equation: `|[x+a, b, c], [c, x+b, a], [a ,b, x+c]|=0`

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`|{:(x+a,x,x),(x,c+a,x),(x,x,x+a):}\|=0, ane0`
`rArr" "|{:(3x+a,x,x),(3x+a,x+a,x),(3x+a,x,x+a):}\|=0(C_(1)toC_(1)+C_(2)+C_(3))`
`rArr" "(3x+a)|{:(1,x,x),(1,x+a,x),(1,x,x+a):}|=0`
`rArr" "(3x+a)|{:(1,x,x),(1,x+a,x),(1,x,x+a):}|=0`
`(R_(2)toR_(2)-R_(2),R_(3)toR_(3)-R_(1))`
`rArr" "(3x+a) a^(2)=0= rArr 3x+a=0 because (a ne 0)`
`rArr" "x=-a/3`
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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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  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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  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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