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

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

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

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  2. If A=[1 3 2 1] , find the determinant of the matrix A^2-2A .

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

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  4. If |[x-2 ,-3], [3x, 2x]|=3 , find the values of x

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  5. Let |[3,y],[x,1]|=|[3,2],[4,1]| Find possible values of x and y if x,y...

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  6. Evaluate the determinant =|((log)3 512,(log)4 3),((log)3 8,(log)4 9)...

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  7. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

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  8. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

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  9. If [ ] denotes the greatest integer less than or equal to the real nu...

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  10. Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),...

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  11. Write the minors and cofactors of each element of the first column o...

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  12. Write the minors and cofactors of each element of the first column o...

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  13. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

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  14. Evaluate the following determinants: |[x-7, x],[5,x+1]| (ii) |[cos...

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  15. Evaluate: |[2, 3, 7], [13, 17, 5], [15, 20, 12]|^2 .

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  16. Show that |[sin10,-cos10],[sin80,cos80]|=1

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  17. Evaluate |[2, 3,-5], [7, 1,-2], [-3, 4 ,1]| by method.

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  18. Evaluate: =|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha,-si...

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  19. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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  20. If A=[[2, 5], [2, 1]] and B=[[4,-3], [2, 5]] , verify that |A B|=|A||B...

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