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Express the matrix A=[{:(3,1),(5,-1):}] ...

Express the matrix `A=[{:(3,1),(5,-1):}]` as the sum of a symmetric and a skew -symmetric matrices .

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Symmetric matrix `=[{:(3,3),(3,-1):}]`, Skew - symmetric matrix `=[{:(0,-2),(2,0):}]`
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ARIHANT PUBLICATION-MATRICES -CHAPTER PRACTICE (Very Short Answer Type Questions)
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  3. Express the matrix A=[{:(3,1),(5,-1):}] as the sum of a symmetric and...

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  4. If possible then find the value of BA and AB , where A=[{:(2,1,2),(1,2...

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  5. A=[{:(3,-4),(1,1),(2,0):}]andB=[{:(2,1,2),(1,2,4):}], then verify that...

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  6. If A=[{:(,),(,):}]andB=[{:(,),(,):}] , then find the matrices A^(2),B^...

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  7. If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}], then show that (A+B)(A-...

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  8. If A=[{:(2,1):}],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}] t...

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  9. If A=[{:(0,6,7),(-6,0,8),(7,-8,0):}],B=[{:(0,1,1),(1,0,2),(1,2,0):}]an...

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  10. How many different matrix products can you form with these three matri...

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  11. Solve the matrix [{:(x,-5,-1):}][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4...

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  12. If A(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}], then prove...

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  13. If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , then find the va...

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  14. If [{:(2,1,3):}][{:(-1,0,-1),(-1,1,0),(0,1,1):}][{:(1),(0),(-1):}]=A ...

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  15. Find the matrix A satisfying the equation [{:(2,1),(3,2):}].A.[{:(-3...

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  16. If A=[{:(1,0,2),(0,2,1),(2,0,3):}], then prove that A is a root of th...

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  17. Let A=[{:(2,3),(-1,2):}]andf(x)=x^(2)-4x+7 . Show that f(A)=O. Use thi...

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  18. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] , then find A^(2)-5A+6I.

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  19. If A=[{:(2,3),(1,2):}], then prove that A^(3)-4A^(2)+A=O.

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  20. If A=[{:(1,0),(-1,7):}], thenfind k such that A^(2)-8A+kI=O.

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