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

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

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To solve the equation given by the product of matrices, we will follow these steps: ### Step 1: Define the Matrices Let: - Matrix A = \(\begin{pmatrix} x & 4 & 1 \end{pmatrix}\) (1x3 matrix) - Matrix B = \(\begin{pmatrix} 2 & 1 & 2 \\ 1 & 0 & 2 \\ 0 & 2 & -4 \end{pmatrix}\) (3x3 matrix) - Matrix C = \(\begin{pmatrix} x \\ 4 \\ -1 \end{pmatrix}\) (3x1 matrix) ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [1\ \ 1\ \ x][1 0 2 0 2 1 2 1 0][1 1 1]=0 , find xdot

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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