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Find the matrix A such that : [(1 ,0 ),(...

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

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To find the matrix \( A \) such that \[ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} A = \begin{pmatrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{pmatrix}, \] we can follow these steps: ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I3=O .

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

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

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

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

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

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

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

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

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

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

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  13. If A=[(1 ,1),( 0, 1)] , prove that A^n=[(1,n),(0, 1)] for all positive...

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  14. If A=[(a, b),(0, 1)] , prove that A^n=[(a^n ,b((a^n-1)/(a-1))),(0, 1)]...

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  15. If A=[(costheta,isintheta),(isintheta,costheta)] , then prove by pri...

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  16. If A=[(cosalpha+sinalpha,sqrt(2)sinalpha),(-sqrt(2)sinalpha,cosalpha-s...

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  17. If A=[(1, 1, 1),( 0, 1, 1), (0, 0, 1)] , then use the principle of m...

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  18. If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=...

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  19. If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n)...

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  20. If A is a square matrix, using mathematical induction prove that (A...

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