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Express the matrix [3-2-4 3-2-5-1 1 2] a...

Express the matrix `[3-2-4 3-2-5-1 1 2]` as the sum of a symmetric and skew-symmetric matrix.

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To express the matrix \[ A = \begin{bmatrix} 3 & -2 & -4 \\ 3 & -2 & -5 \\ -1 & 1 & 2 \end{bmatrix} ...
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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If [[xy, 4],[z+6, x+y]]=[[8, w],[0, 6]], write the value of (x+y+z)dot

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  2. If A=[a(i j)] is a skew-symmetric matrix, then write the value of sumi...

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  3. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

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  4. Show that the elements on the main diagonal of a skew-symmetric matrix...

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  5. If A is a skew-symmetric and n in N such that (A^n)^T=lambdaA^n , wri...

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  6. If A is a skew-symmetric matrix and n is an odd natural number, write ...

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  7. Show that the matrix B^TA B is symmetric or skew-symmetric according a...

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  8. If A is a symmetric matrix and n in N , write whether A^n is symmetri...

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  9. If S=[S(i j)] is a scalar matrix such that s(i i)= k and A is a square...

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  10. If A is a square matrix, using mathematical induction prove that (A^T)...

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  11. If A and B are square matrices of the same order such that A B=B A , t...

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  12. There are 2 families A and B. There are 4 men, 6 women and 2 children ...

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  13. If A={:[(-1),(2),(3)]:} and B=[-2" "-1" "-4] then verify that (AB)^(T)...

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  14. If: [(xy,5x) , (z+6,y^2+1)]=[(8,w),(0,6)], then find the values of x ,...

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  15. The sales figure of two car dealers during January 2013 showed that ...

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  16. If A^T=[[3, 4],[-1, 2], [0 ,1]] and B=[[-1, 2, 1],[ 1, 2, 3]], find A^...

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  17. If l1,""""m1,""""n1 and l2,""""m2,""""n2 are the direction cosines ...

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

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  19. Construct a3×2m a t r i xA=[a(i j)] whose elements are given by a(i j...

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  20. For what values of x and y such that matrices A and B are equal ? ...

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