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If [1\ \ 1\ \ x][1 0 2 0 2 1 2 1 0][1 1 ...

If `[1\ \ 1\ \ x][1 0 2 0 2 1 2 1 0][1 1 1]=0` , find `xdot`

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Given that,
`[(1,1,x)][(1,0,2),(0,2,1),(2,1,0)][(1),(1),(1)]=0`
`=>[(1+0+2x,0+2+x,2+1)][(1),(1),(1)]=0`
`=>[(1+2x,2+x,3)][(1),(1),(1)]=0`
`=>[1+2x+2+x+3]=0`
`=>3x+6=0`
`=>3x=-6`
`=>x=-2`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)] , show that A^2=A .

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  2. If A=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)] , show that A^2=I3

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  3. If [1\ \ 1\ \ x][1 0 2 0 2 1 2 1 0][1 1 1]=0 , find xdot

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  4. If [(2,3),(5,7)][(1,-3),(-2,4)]=[(-4,6),(-9,x)] , find xdot

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  5. If [(x,4,1)][(2,1,2),(1,0,2),(0,2,-4)][(x),(4),(-1)]=0 , find xdot

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  6. If [(1, -1,x)][(0 ,1,-1),( 2 ,1 ,3),( 1 ,1 ,1)][(0),( 1),( 1)]=0 , fin...

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  7. If A=[(3,-2),( 4,-2)] and I=[(1 ,0),( 0 ,1)] , then prove that A^2-A+2...

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  8. If A=[(3 ,1),(-1, 2)] and I=[(1, 0), (0 ,1)] , then find lambda so tha...

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  9. If A=[[3 ,1],[-1, 2]] , show that A^2-5A+7I2=O .

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  10. If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I2=O .

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  11. Show that the matrix A=[(2, 3), (1, 2)] satisfies the equation A^3-4A...

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  12. Show that the matrix A=[(5, 3), (12 ,7)] is a root of the equation A...

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  13. If A=[(3,-5),(-4, 2)] , find A^2-5A-14 Idot

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  14. If A=[(3, 1),(-1, 2)] , show that A^2-5A+7I=O . Use this to find A^4

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  15. If A=[(3,-2) ,(4,-2)] , find k such that A^2-k A-2I2=0 .

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  16. If A=[(1, 0),(-1 ,7)] , find k such that A^2-8A+k I=O .

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  17. If A=[(1 ,2 ),(2, 1)] and f(x)=x^2-2x-3 , show that f(A)=O .

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  18. If A=[(2, 3),( 1, 2)] and I=[(1, 0),( 0, 1)] , then find lambda,mu ...

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  19. Find the value of x for which the matrix product [(2, 0, 7),( 0, ...

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  20. Solve the matrix equations: [(0, 2, 1)][(1, 2, 0),( 2 ,0 ,1 ),(1 ,0...

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