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Solve the matrix equations: [(x,-5,-1)...

Solve the matrix equations: `[(x,-5,-1)][(1, 0, 2) ,( 0,2 ,1),( 2, 0, 3)][(x),(4),( 1)]=0`

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Given that,
`[(x,-5,-1)][(1, 0, 2) ,( 0,2 ,1),( 2, 0, 3)][(x),(4),( 1)]=0`
`implies [(x,-5,-1)][(x+2),(9),(2x+3)]=0`
`implies [x^2+2x-45-2x-3]=0`
`implies[x^2-48]=0`
`implies x^2=48`
`implies x=pm4sqrt3`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Find the value of x for which the matrix product [(2, 0, 7),( 0, ...

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

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  3. Solve the matrix equations: [(x,-5,-1)][(1, 0, 2) ,( 0,2 ,1),( 2, 0,...

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

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

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

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  7. If A=[(1 ,0, 2), (0, 2, 1), (2, 0, 3)] , then show that A is a root of...

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

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

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

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

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

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  13. Find a 2xx2 matrix A such that A[(1,-2),( 1, 4)]=6I2 .

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

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

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

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

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

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  19. If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)...

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  20. If A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)] , find A^2-5A+4I and hence fi...

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