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If [(2x+y,3y),(0, 4)]=[(6, 0),( 6, 4)] ...

If `[(2x+y,3y),(0, 4)]=[(6, 0),( 6, 4)]` , then find `x` .

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To solve the matrix equation \(\begin{pmatrix} 2x+y & 3y \\ 0 & 4 \end{pmatrix} = \begin{pmatrix} 6 & 0 \\ 6 & 4 \end{pmatrix}\), we need to equate the corresponding elements of both matrices. ### Step 1: Set up the equations From the matrix equation, we can extract the following equations by equating corresponding elements: 1. \(2x + y = 6\) (from the first row, first column) 2. \(3y = 0\) (from the first row, second column) 3. \(0 = 6\) (from the second row, first column) ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Find the value of x , if [(3x+y,-y),(2y-x,3)]=[(1, 2),(-5, 3)] .

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  2. If matrix A=[1,2,3] , find AA^T .

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  3. If [(2x+y,3y),(0, 4)]=[(6, 0),( 6, 4)] , then find x .

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  4. If A=[(1, 2 ),(3, 4)] , find A+A^T .

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  5. If [(a+b,2),( 5,b)]=[(6, 5),( 2, 2)] , then find adot

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  6. If A is a matrix of order 3xx4 and B is a matrix of order 4xx3 , find ...

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  7. If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] is identity matrix, t...

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  8. If [(1, 2),( 3, 4)][(3, 1),( 2, 5)]=[(7, 11),( 23, k)] , then write t...

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  9. If I is the identity matrix and A is a square matrix such that A...

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  10. If A=[(1, 2),( 0, 3)] is written as B+C , where B is a symmetric matri...

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  11. If A is 2 times 3 matrix and B is a matrix such that A^T\ B and B A^T ...

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  12. What is the total number of 2xx2 matrices with each entry 0 or 1...

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  13. If [[x,x-y],[2x+y,7]]=[[3 ,1],[ 8, 7]] , then find the value of y

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  14. If a matrix has 5 elements, write all possible orders it can have.

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  15. For a 2xx2 matrix A=[a(i j)] whose elements are given by a(i j)=i/j...

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  16. If x [[2 ],[3]]+y[[-1],[ 1]]=[[10],[ 5]] , find the value of x

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  17. If [[9,-1, 4],[-2, 1, 3]]=A+[[1 ,2,-1],[ 0, 4, 9]] , then find matrix ...

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  18. If [(a-b,2a+c),(2a-b,3c+d)]=[(-1, 5),( 0, 13)] , find the value of b

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  19. For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-...

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  20. If matrix A=[[2,-2],[-2, 2]] and A^2=p A , then write the value of p

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