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Prove that the determinant |[x, sinthet...

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

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. A determinant of second order is made with the elements 0 and 1. Fi...

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  2. If a ,b , c are nonzero real numbers such that |[b c,c a, a b],[ c a, ...

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  3. Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[...

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  4. Consider the determinant f(x)=|[0,x^2-a, x^3-b], [x^2+a,0,x^2+c], [x^4...

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  5. Find the value of |[1, 2, 4],[-1,3, 0],[4 ,1, 0]|

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  6. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

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  7. If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a ...

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  8. Each question has four choices a, b, c and d, out of which only one is...

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  9. If a ,b ,c in R , then find the number of real roots of the equat...

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  10. Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by ...

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  11. Without expanding at any stage, prove that the value of each of the...

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  12. If a,b c(all positive)are the p th,q thand r th terms repectively of a...

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  13. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

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  14. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

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  15. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

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  16. If a1b1c1,a2b2c2 and a3b3c3 are three digit even natural numbers and ...

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  17. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

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  18. The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...

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  19. Show that the determinant |a^2+b^2+c^2 bc+ca+ab bc+ca+ab bc+ca+ab a^2+...

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  20. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

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