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If A=[(1,tanx),(-tanx,1)], Show that, A^...

If `A=[(1,tanx),(-tanx,1)]`, Show that, `A^TA^-1=[(cos2x,-sin2x),(sin2x,cos2x)]`.

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
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  2. If A and B are matrices of order 3 such that abs[A]=-1,abs[B]=3,then...

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  3. If A=[(1,tanx),(-tanx,1)], Show that, A^TA^-1=[(cos2x,-sin2x),(sin2x,c...

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  4. If A=[[1,1,5],[0,1,3],[0,-1,-2]] what is the value of abs[3A]?

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  5. Find the equation of the line joining the points(1,2) and (-3,-2) us...

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  6. Find the values of x in which abs[[3,x],[x,1]]=abs[[3,2],[4,1]]

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  7. Using the property of determinants,show that the points A(a,b+c),B(b...

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  8. Examine the consistency of system of following equations: 5x-6y+4z...

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  9. If A=[[3,-2,3],[2,1,-1],[4,-3,2]] Find abs[A]

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  10. If A=[[3,-2,3],[2,1,-1],[4,-3,2]] Find A^-1

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  11. If A=[[3,-2,3],[2,1,-1],[4,-3,2]] Solve the linear equations 3x-2y...

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  12. Arjun' purchased 3 pens,2 purses and 1 instrument box and pays Rs. 410...

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  13. Arjun' purchased 3 pens,2 purses and 1 instrument box and pays Rs. 4...

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  14. Write the value of x+y+z, if [(1,0,0),(0,1,0),(0,0,1)][(x),(y),(z)]=[(...

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  15. Using properties of determinants prove the following. abs[[b+c,a,...

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  16. Consider the points (b,c+a),(c,a+b) and (a,b+c). Find the area of the ...

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  17. Consider the points (b,c+a),(c,a+b) and (a,b+c). Are the given points ...

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  18. If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)] Perform R1rarrR1+...

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  19. If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)]Perform R1rarrR1+R...

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  20. Using properties of determinants prove the following. abs[[a-b-c,...

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