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Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: `A=[[5 ,20],[ 0,-1]]` (ii) `A=[[-1, 4],[ 2, 3]]` (iii) `A=[[1,-3, 2],[ 4,-1, 2],[ 3, 5, 2]]` (iv) `A=[[1,a, bc],[1,b, c a],[1,c, a b]]`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If [ ] denotes the greatest integer less than or equal to the real nu...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Find the values of x , if |[2, 4], [5, 1]|=|[2x,4], [6,x]|

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  15. Find the values of x , if |[3x,7], [2, 4]|=10

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  16. Find the integral value of x , if |[x^2,x,1],[ 0, 2, 1],[ 3, 1, 4]...

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  17. For what value of x the matrix A is singular? A=[[1+x,7], [3-x,8]]

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  18. Without expanding evaluate the determinant |41 1 5 79 7 9 29 5 3|

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  19. If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2,...

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  20. Show that |[1,a ,b+c],[1,b, c+a],[1,c ,a+b]|=0 .

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