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Evaluate Delta=|{:(0,sinalpha,-cosalpha)...

Evaluate `Delta=|{:(0,sinalpha,-cosalpha),(-sinalpha,0,sinbeta),(cosalpha,-sinbeta,0):}|`

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Evaluate |{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}|

Using properties of determinants in Exercise 11 to 15 prove that |{:(sinalpha,cosalpha,cos(alpha+delta)),(sinbeta,cosbeta,cos(beta+delta)),(singamma,cosgamma,cos(gamma+delta)):}|=0

If (i) A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] then verify that A'A=I. (ii) A=[{:(sinalpha,cosalpha),(-cosalpha,sinalpha):}] then verify that A'A=I.

Find the inverse of each of the following matrices (if it exits) given in example number 5 to 11 [{:(1,0,0),(0,cosalpha,sinalpha),(0,sinalpha,-cosalpha):}]

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) , then show that sinalpha+cosalpha=sqrt(2)costheta .

If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}],andA^(-1)=A' , find value of alpha .

If A=[{:(0,"tan"(alpha)/(2)),("tan"(alpha)/(2),0):}] and I theidentity matrix of order 2, show that I+A=(I-A)[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}] .

If A(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] then prove that A(alpha)A(-alpha)=I .

If theta+beta=alphaandsintheta=ksinbeta then prove that tantheta=(ksinalpha)/(1+kcosalpha)andtanbeta=(sinalpha)/(k+cosalpha) .

KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. Evaluate {:[(x, x+1),(x-1 ,x)]:}

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  2. Evaluate the deternminant Delta=|{:(1,2,4),(-1,3,0),(4,1,0):}|

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  3. Evaluate Delta=|{:(0,sinalpha,-cosalpha),(-sinalpha,0,sinbeta),(cosalp...

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  4. Find values of x for which |{:(3,x),(x,1):}|=|{:()3,2),(4,1):}|

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  5. Verify: The value of the determinant remains unchanged if its rows and...

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  6. Verify Property 2 for Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|

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  7. Evaluate Delta =|{:(3,2,3),(2,2,3),(3,2,3):}|

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  8. Evaluate {:[( 102,18,36),( 1,3,4),( 17,3,6)]:}

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  9. Using the property of determinants and without expanding prove the fol...

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  10. Prove that |{:(a,a+b,a=b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}...

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  11. Without expanding prove that Delta=|{:(x+y,y+z,z+x),(z,x,y),(1,1,1):...

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  12. Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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  13. Prove that {:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:}

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  14. If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z...

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  15. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

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  16. Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1...

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  17. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  18. Find the minor of elements 6 in the determinant Delta=|{:(1,2,3),(4,...

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  19. Find minors and cofactors of all the elements of the determinant |{:(1...

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  20. Find minors and cofactors of the elements a(11),a(21) in the determina...

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