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If A=|{:(3,5),(2,4):}|, find A^(-1)....

If `A=|{:(3,5),(2,4):}|`, find `A^(-1)`.

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`|A|=|{:(3,5),(2,4):}|`
=12-10
`=2ne0`
`rArr" "A is invertible.`
`"Now"" "C_(11)=(-1)^(1+1).4=4`
`C_(12)=(-1)^(1+2).42=-2`
`C_(21)=(-1)^(2+1).5=-5`
`C_(22)=(-1)^(2+3).3=3`
` therefore"adj.A="[{:(C_(11),C_(12)),(C_(21),C_(22)):}]=[{:(4,-2),(-5,3):}]=[{:(4,-5),(-2,3):}]`
`therefore"adj.A^=1/(|A|)."adj.A=1/2[{:(4,-5),(-2,3):}]`
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NAGEEN PRAKASHAN-DETERMINANTS-Miscellaneous Exercise
  1. If A=|{:(3,5),(2,4):}|, find A^(-1).

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  2. Prove that the determinant [xsinthetacostheta-sintheta-x1costheta1x]is...

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  3. Show without expanding at any stage that: [a,a^2,bc],[b,b^2,ca],[c,c^...

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  4. Evaluate abs[{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta...

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  5. 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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  6. Solve the equation: |[x+a, b,c],[a,x+b,c],[a,b,x+c]|=0

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  7. Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^...

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  8. 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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  9. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}]. Verify that ltbtgt (i) [adjA]^...

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  10. Evaluate: [[x,y,x+y],[y,x+y,x],[x+y,x,y]]

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  11. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

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  12. Using peoperties of determinants in questions 11 to 15, prove that : ...

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  13. Prove that [[x, x^2 , 1+px^3], [y, y^2, 1+py^3] ,[z, z^2, 1+pz^3]] = (...

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  14. Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

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

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

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  17. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

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  18. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

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  19. Choose the correct answer in questions 17 to 19: If x, y, z are non...

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  20. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

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