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Express the matrix [{:(2 ,1),(3,4):}] as...

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

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To express the matrix \( A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \) as the sum of a symmetric matrix and a skew-symmetric matrix, we can follow these steps: ### Step 1: Define the matrix A Let \[ A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \] ...
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NCERT EXEMPLAR-MATRICES-Matrices
  1. z, if A='[{:(0,2y,z),(x,y,-z),(x,-y,z):}] satisfy A'=A^(-1)

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  2. If possible using elementary row transformations, find the inverse of ...

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

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

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

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

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  7. If A=1/pi[sin^(-1)(pix)tan^(-1)(x/pi)sin^(-1)(x/pi)cot^(-1)(pix)] and ...

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  8. If A and B are two matrices of the order 3 xx m and 3 xx n, respective...

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  9. If A=[{:(0,1),(1,0):}] then A^(2) is equal to

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  10. If matrix A=[a(ij)](2X2), where a(ij)={[1,i!=j],[0,i=j]}, then A^2 i...

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  11. The matrix [{:(1,0,0),(0,2,0),(0,0,4):}] is a

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  12. The matrix [{:(0,-5,8),(5,0,12),(-8,-12,0):}] is a

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  13. If A is matrix of order mxxn and B is a matrix such that AB' and B'A ...

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  14. if A and B are matrices of same order, then (AB'-BA') is a 1) null mat...

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

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  16. For any two matrices A and B , we have

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  17. On usign elementry column operation C(2)rArrC(2)-2C(1) in the followin...

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  18. On using row operation R(1)rArrR(1)-3R(2) in the following matrix equa...

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  19. ......... Matrix is both symmetric and skew-symmetric matrix.

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  20. Sum of two skew-symmetric matrices is always ......... Matrix.

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