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Evaluate: =|[0,sinalpha,-cosalpha],[-sin...

Evaluate: `=|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha,-sinbeta,0]|`

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Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sinalpha,0,sinbeta],[cosalphas-sinbeta,0]|=0

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If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

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Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

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Show without expanding at any stage that: | (1,cosalpha-sinalpha, cosalpha+sinalpha),(1,cosbeta-sinbeta,cosbeta+sinbeta),(1, cosgamma-singamma,cosgamma+singamma)| =2 |(1,cosalpha, sinalpha),(1,cosbeta, sinbeta),(1,cosgamma,singamma)|

Evaluate |{:(cos alpha cos beta,,cos alphasinbeta,,-sinalpha),(-sinbeta,,cos beta,,0),(sinalpha cos beta,,sinalphasinbeta,,cos alpha):}|

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Show that |[sin10,-cos10],[sin80,cos80]|=1

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

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

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

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

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

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

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

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

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

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

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

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

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  14. 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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  15. 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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  16. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

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

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

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  19. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

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  20. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

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