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Evaluate the following determinants: |[x...

Evaluate the following determinants: `|[x-7, x],[5,x+1]|` (ii) `|[costheta ,-sintheta],[sintheta,costheta]|` `|[cos15^0,sin15^0],[sin75^0,cos75^0]|` (iv) `|[a+i b, c+i d],[-c+i d, a-i b]|`

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Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sinthetasinthetacostheta| |cos15^0sin15^0sin75^0cos75^0| (iv) |a+i b c+i d-c+i d a-i b|

Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sinthetasinthetacostheta| |cos15^0sin15^0sin75^0cos75^0| (iv) |a+i b c+i d-c+i d a-i b|

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Evaluate the determinants in(i) |(costheta,-sintheta),(sintheta,costheta)| (ii) |(x^2-x+1,x-1),(x+1,x+1)|

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If A=[[cos theta , sin theta],[sin theta,-costheta]], B = [[1,0],[-1,1]], C=ABA^(T), then A^(T) C^(n) A, n in I^(+) equals to

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Write the minors and cofactors of each element of the first column o...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. 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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  19. 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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  20. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

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