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Evaluate triangle = |[0,sinalpha,-cosalp...

Evaluate `triangle = |[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha,-sinbeta,0]|`

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Without expanding show that |(0,sinalpha, -cosalpha),(-sinalpha,0,sinbeta),(cosalpha, -sinbeta,0)| = 0

Evaluate |[cosalphacosbeta,cosalphasinbeta,-sinalpha],[-sinbeta,cosbeta,0],[sinalphcosbeta,sinalphasinbeta,cosalpha]|

Using properties of determinants, prove that: |[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]| = 0

If A = {:[(cosalpha, sinalpha),(-sinalpha, cosalpha)] , then find A^2

Find A^2 if A = [(cos alpha, sinalpha),(-sin alpha, cos alpha)]

Prove that: (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)

For the matrix A = [(cos alpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0,0,1)] , verify that A (adj A) = |A| I.

Let F(alpha)={:[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1)] and G(beta) = [(cosbeta,0,sinbeta),(0,1,0),(-sinbeta,0,cosbeta)] . Show that [F(alpha).G(beta)]^-1=G(-beta),F(-alpha)

PSEB-DETERMINANTS-Exercise
  1. Evaluate triangle = |[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cos...

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  2. Evaluate the determinant : |[2,4],[-5,-1]|

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  3. Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

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  4. Evaluate the determinant : |[x^2-x+1,x+1],[x+1,x+1]|

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  5. If A = [[1,2],[4,2]], then show that |2A| = 4|A|

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  6. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

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  7. Evaluate the determinant : |[3,-1,-2],[0,0,-1],[3,-5,0]|

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  8. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

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  9. Evaluate the determinant : |[0,1,2],[-1,0,-3],[-2,3,0]|

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  10. Evaluate the determinant : |[2,-1,-2],[0,2,-1],[3,-5,0]|

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  11. If A = [[1,1,-2],[2,1,-3],[5,4,-9]], find |A|

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  12. Find values of x, if : |[2,4],[5,1]| = |[2x,4],[6,x]|

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  13. Find values of x, if : |[2,3],[4,5]| = |[x,3],[2x,5]|

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  14. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  15. Using the property of determinants and without expanding , prove that:...

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  16. Using the property of determinants and without expanding , prove that:...

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  17. Using the property of determinants and without expanding , prove that:...

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  18. Using the property of determinants and without expanding , prove that:...

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  19. Using the property of determinants and without expanding , prove that:...

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  20. Using the property of determinants and without expanding , prove that:...

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  21. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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