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

If `[(1, -1,x)][(0 ,1,-1),( 2 ,1 ,3),( 1 ,1 ,1)][(0),( 1),( 1)]=0` , find `x`

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given that,
`[(1,-1,x)][(0 ,1,-1),( 2 ,1 ,3),( 1 ,1 ,1)][(0),( 1),( 1)]=0`
`=>[(1,-1,x)][(0+1-1),(0+1+3),(0+1+1)]=0`
`=>[(1,-1,x)][(0),(4),(2)]=0`
`=>0-4+2x=0`
`=>2x=4`
`=>x=2`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [(2,3),(5,7)][(1,-3),(-2,4)]=[(-4,6),(-9,x)] , find xdot

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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