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If `X` and `Y` are `2xx2` matrices, then solve the following matrix equations for `X` and `Y` `2X+3Y=[[2,3],[4,0]],3X+2Y=[[-2,2],[1,-5]]`

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To solve the given matrix equations for matrices \(X\) and \(Y\), we start with the equations: 1. \(2X + 3Y = \begin{pmatrix} 2 & 3 \\ 4 & 0 \end{pmatrix}\) (Equation 1) 2. \(3X + 2Y = \begin{pmatrix} -2 & 2 \\ 1 & -5 \end{pmatrix}\) (Equation 2) ### Step 1: Multiply Equation 1 by 3 We multiply the entire first equation by 3: ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[1-1 2 3],B=[2 1 1 0],p rov et h a t(A+B)^2!=A^2+2A B+B^2

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  2. Find a matrix X such that 2A+B+X=0 , where A= [-1 2 3 4],B=[3-2 1 5] ...

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  3. If X and Y are 2xx2 matrices, then solve the following matrix equat...

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  4. If A=[[alpha, 0], [1, 1]] and B=[[1 ,0],[ 5 ,1]], find the values of a...

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  5. Find the value of x such that [[1, x, 1]][[1 ,3, 2],[2, 5 ,1],[ 15 ,3 ...

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  6. If A=[[1,-1],[2,-1]],B=[[a,1],[b, -1]] and (A+B)^2=A^2+B^2, find the v...

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  7. If A= [[0, 1],[-1, 0]], find xand y such that (x I+y A)^2=A

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  8. If [(2,-1),(1,0),(-3,4)]A=[(-1,-8,-10),(1,-2,-5),(9,22,15)], find A.

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  9. Let f(x)=x^2-5x+6. Find f(A), if A=[[2, 0 ,1],[2, 1, 3],[ 1,-1, 0]]

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  10. If A and B are symmetric matrices of the same order, write whether AB-...

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  11. If A is a square matrix such that A^2=A ,then (I+A)^3-7A is equal to

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  12. If A is a square matrix such that A^2=A , then write the value of 7A-(...

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  13. Construct a 3xx4 matrix A=[a(i j)] whose elements are given by (i)a...

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  14. If [x-y2x+z2x-y3z+w]=[-1 5 0 13] , find x ,\ y ,\ z ,\ wdot

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  15. Find the values of x ,\ y ,\ z and a which satisfy the matrix equ...

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  16. A matrix has 12 elements. What are the possible orders it can have?

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  17. If A=[a(i j)] is a matrix given by A=[a(i j)]=[4 5 21\ \ -2 7 15\ \ 1 ...

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  18. A matrix has 12 elements. What are the possible orders it can have?

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  19. Construct a 2xx2 matrix A=[a(i j)] whose elements are given by a(i ...

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  20. Construct a 2xx3 matrix A=[a(i j)] whose elements are given by a(i ...

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