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

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

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Evaluate the following determinants: |[x-7, x],[5,x+1]| (ii) |[cos...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

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  17. Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

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  18. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

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  19. Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2th...

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  20. Find the value of the determinant =|(2, 3, 4) ,(5, 6, 8),( 6x,9x, 12...

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