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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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Prove that the determinant Delta =|{:(x,,sintheta,,cos theta),(-sin theta,,-x,,1),(cos theta,,1,,x):}| is independent of theta .

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

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Evaluate the determinants in |{:(costheta,-sintheta),(sintheta,costheta):}|

If sintheta+costheta=x then sintheta-costheta=?

Evaluate the determinates abs([-costheta,-sin theta],[sintheta,-costheta])

Let triangle1=|{:(x,sintheta,costheta),(-sintheta,x,1),(costheta,1,x):}| and triangle2=|{:(x,sin2theta,cos2theta),(-sin2theta,x,1),(cos2theta,1,x):}| then which of following is/are true?

MODERN PUBLICATION-DETERMINANTS-Miscellaneous Exercise on Chapter 4
  1. Prove that the determinant |{:(x,sintheta,costheta),(-sintheta,-x,1),(...

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  2. Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b...

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

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  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

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  5. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  6. Prove that |a^2b c a c+c^2a^2+a bb^2a c a bb^2+b cc^2|=4a^2b^2c^2 .

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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,x],[x+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 peoperties of determinants in questions 11 to 15, prove that : ...

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  12. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  13. Using properties of determinants, prove the following: |3"a"-"a"+"...

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  14. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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  15. Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, ...

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  16. 2/x+3/y+10/z=4, 4/x-6/y+5/z=1, 6/x+9/y-20/z=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. Choose the correct answer in questions 17 to 19: If x, y, z are non...

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  19. Let A=[(1,sintheta, 1),(-sintheta, 1, sintheta),(-1, -sintheta, 1)], w...

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