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If A = [[1,2],[4,2]] then show that |2A|...

If A = `[[1,2],[4,2]]` then show that |2A|= 4|A|

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V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Evaluate |[2,4],[-5,-1]|

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  2. Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|

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  3. If A = [[1,2],[4,2]] then show that |2A|= 4|A|

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  4. If A=[[1, 0, 1],[ 0, 1, 2],[ 0, 0, 4]] then show that |3 A|=27...

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  5. Evaluate the determinants (i) |[3 , -1, -2],[ 0, 0, -1],[ 3, -5,...

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  6. If A = [(1,1,-2),(2,1,-3),(5,4,-9)]. Find |A|

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  7. Find values of x if i) |[2 , 4],[ 5, 1]|=|[2 x, 4], [6, x]| ii) ...

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  8. If |[x ,2],[ 18, x]|=|[ 6, 2 ],[ 18, 6]|, then x is equal to a)6 ...

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  9. Verify Property 1 for Delta=|[2 ,-3, 5],[ 6, 0, 4],[ 1, 5, -7]...

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  10. Verify Property 2 for Delta=|[2 , -3, 5],[ 6, 0, 4],[ 1, 5, -7]...

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  11. Evaluate Delta=|[3, 2, 3],[ 2, 2, 3],[ 3, 2, 3]|

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  12. Evaluate |[102, 18, 36],[ 1, 3, 4],[ 17, 3, 6]|

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  13. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  14. Prove that |[a, a+b, a+b+c],[ 2 a, 3 a+2 b, 4 a+3 b+2 c],[ 3 a, ...

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  15. Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

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  16. Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|

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  17. Using properties of determinants prove the following. abs[[b+c,a,...

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  18. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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  19. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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  20. Without expanding the determinant prove the following. |[x,a,x+a],[y...

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