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Find the value of x for which the matri...

Find the value of `x` for which the matrix product `[(2, 0, 7),( 0, 1, 0),( 1,-2, 1)][(-x, 14 x,7x),(0, 1, 0),(x,-4x,-2x)]` equal to an identity matrix.

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Given that,
`[(2, 0,7),(0,1,0),(1,- 2,1)][(-x,14x,7x),(0,1,0),(x,-4x,-2x)]=[(1,0,0),(0,1,0),(0,0,1)]`
`implies [(-2x+7x,28x-28x,14x-14x),(0,1,0),(-x+x,14x-2-4x,7x-2x)]= [(1,0,0),(0,1,0),(0,0,1)]`
`implies [(5x,0,0),(0,1,0),(0,10x-2,5x)]= [(1,0,0),(0,1,0),(0,0,1)]`
`implies x=1/5`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
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  2. If A=[(2, 3),( 1, 2)] and I=[(1, 0),( 0, 1)] , then find lambda,mu ...

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

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

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  6. If A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)] , compute A^2-4A+3I3 .

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  7. If f(x)=x^2-2x , find f(A), where A=[(0, 1, 2),( 4 ,5, 0 ),(0, 2 ,3)...

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  8. If f(x)=x^3+4x^2-x , find f(A) , where A=[(0 ,1, 2 ),(2,-3 ,0),( 1,-...

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  10. If A=[(1, 2 ,2 ),(2 ,1 ,2),( 2 ,2, 1)] , then prove that A^2-4A-5I=O ...

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  11. If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I3=O .

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  12. Without using the concept of inverse of a matrix, find the matrix [...

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  13. Find the matrix A such that : [(1 ,0 ),(0 ,1)]A=[(3 ,3 ,5 ),(1, 0 ,1)]

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  14. Find the matrix A such that : [2, 1, 3][(-1,0,-1),(-1,1 ,0 ),(0 ,1, 1...

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  16. If A=[(0, 0), (4, 0)] , find A^(16) .

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  17. If A=[(0,-x),(x,0)] , B=[(0 ,1 ),(1 ,0)] and x^2=-1 , then show tha...

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  18. If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I...

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  19. If A=[(3,-5),(-4, 2)] , then find A^2-5A-14 I .

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  20. If P(x)=[cosxsinx-sinxcosx] , then show that P(x)\ P(y)=P(x+y)=P(y)\ P...

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