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Compute the elements a(43) and a(22) of ...

Compute the elements `a_(43)` and `a_(22)` of the matrix: `A=[(0 ,1, 0),( 2, 0 ,2 ),(0,3,2),(4 ,0, 4)] [(2,-1),(-3, 2),( 4, 3)][(0, 1,-1, 2,-2 ),(3,-3, 4,-4 ,0)]`

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`A=[(0 ,1, 0),( 2, 0 ,2 ),(0,3,2),(4 ,0, 4)] [(2,-1),(-3, 2),( 4, 3)][(0, 1,-1, 2,-2 ),(3,-3, 4,-4 ,0)]`
`=>A=[(0 ,1, 0),( 2, 0 ,2 ),(0,3,2),(4 ,0, 4)][(0-3,2+3,-2-4,4+4,-4-0),(0+6,-3-6,3+8,-6-8,6+0),(0+9,4-9,-4+12,8-12,-8+0)]`
`=>A=[(0 ,1, 0),( 2, 0 ,2 ),(0,3,2),(4 ,0, 4)][(-3,5,-6,8,-4),(6,-9,11,-14,6),(9,-5,8,-4,-8)]`
`=>A=[(0+6+0,0-9-0,0+11+0,0-14-0,0+6-0),(-6+0+18,10-0-10,-12+0+16,16-0-8,-8+0-16),(0+18+18,0-27-10,0+33+16,0-42-8,0+18-16),(-12+0+36,20-0-20,-24+0+32,32-0-16,-16+0-32)]`
`=>A=[(6,-9,11,-14,6),(12,0,4,8,-24),(36,-37,49,-50,2),(24,0,8,16,-48)]`
so,`a_(43)=8` and `a_(22)=0`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. For the following matrices verify the distributivity of matrix multi...

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  2. If A=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)] , B=[(0 ,5,-4),(-2, 1 ,3),(-1, ...

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  3. Compute the elements a(43) and a(22) of the matrix: A=[(0 ,1, 0),( 2, ...

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  4. If A=[(0 ,1 ,0),( 0, 0, 1),(p, q ,r)] and I is the identity matrix o...

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  5. If omega is a complex cube root of unity, show that ([(1,omega,omega...

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  6. If A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)] , show that A^2=A .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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