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If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6)...

If `[{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}]`, then find the values of x,y,z and w.

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To solve the equation given by the matrices \(\begin{pmatrix} xy & 4 \\ z + 6 & x + y \end{pmatrix} = \begin{pmatrix} 8 & w \\ 0 & 6 \end{pmatrix}\), we will equate the corresponding elements of the matrices. ### Step-by-Step Solution: 1. **Equate the elements of the matrices:** - From the first row and first column: \[ xy = 8 \quad \text{(1)} ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. If A is a square matrix, using mathematical induction prove that (A...

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  2. Find inverse, by elementary row operations (if possible) , of both fo...

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  3. If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}], then find the values of x...

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  4. If A=[{:(1,5),(7,12):}] and B=[{:(9,1),( 7,8):}] then find a matrix C ...

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  5. If A=[{:(3,-5),(-1,2):}] then find A^(2)-5A- 4I.

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  6. Find the values of a,b,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,2...

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  7. Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10)...

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  8. If A=[{:(1,2),(4,1):}] , then find A^(2)+2A+7I.

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  9. If A=[{:(cos alpha,sin alpha),(-sin alpha, cos alpha):}] and A^(-1)=A'...

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  10. If matrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is skew-symmetric matrix, the...

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  11. If P(x)=[(cosx, sinx),(-sinx, cosx)], then show that P(x).P(y)=P(x+y)=...

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  12. If A is square matrix such that A^(2)=A, then show that (I+A)^(3)=7A+I...

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  13. If A, B are square matrices of same order and B is skew-symmetric mat...

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  14. Let A ,B be two matrices such that they commute. Show that for any pos...

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  15. Find A=[(0,2y,z),(x,y,-z),(x,-y,z)] satisfies A^(T) = A^(-1)

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  16. Using elementary transformations (operations), find the inverse of the...

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  17. Express the matrix [{:(2 ,1),(3,4):}] as the sum of a symmetric and a ...

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  18. The matrix P=[{:(0,0,4),(0,4,0),(4,0,0):}] is a

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  19. Total number of possible matrices of order 3xx3 with each entry 2 or 0...

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  20. [{:(2x+y,4x),(5x-7,4x):}]=[{:(7,7y-13),(y,x+6):}] then the value of x,...

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