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Prove that |[x,sintheta, costheta],[-sin...

Prove that `|[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]|` is independent of `theta`

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`x(-x^2-1)+x`, in which independent of `theta`.
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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
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  4. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs.60.The cost of ...

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  5. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  10. Prove that |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^...

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

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  12. Let A=[[1,-2,1],[-2,3,1],[1,1,5]] verify that (A^(-1))^(-1)=A

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  13. Let A=[[1,-2,1],[-2,3,1],[1,1,5]] verify that (A^(-1))^(-1)=A

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  14. Using properties of determinants prove abs[[x,y,x+y],[y,x+y,x],[x+y,...

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  15. evaluate | [1,x,y],[1,x+y,y],[1,x,x+y] |

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  18. Consider a system of linear equations which is given below, 2/x+3/y+10...

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  19. If a,b,c are in A.P., then the determinant |[x+2, x+3, x+2a],[x+3,x+...

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  20. If x,y,z are non-zero real numbers, then the inverse of A=[[x,0,0],[0,...

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