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Without expanding evaluate the determina...

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

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Without expanding evaluate the determinant |sinalphacosalphasin(alpha+delta)sinbetacosbetasin(beta+delta)singammacosgammasin(gamma+delta)| .

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0

Prove that |(sin alpha,cos alpha,sin(alpha+delta)),(sin beta,cos beta,sin(beta+delta)),(sin gamma,cos gamma,sin(gamma+delta))|=0

Without expanding, show that the value of the following determinant is zero: |[sinalpha,cosalpha,cos(a+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]|

Using properties of determinants. Prove that |(sinalpha,cosalpha,cos(alpha+delta)),(sinbeta,cosbeta,cos(beta+delta)),(singamma,cosgamma,cos(gamma+delta))|=0

Without expanding, show that the value of each of the determinants is zero: |sinalphacosalpha"cos"(alpha+delta)sinbetacosbeta"cos"(beta+delta)singammacosgamma"cos"(gamma+delta)|

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 Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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

Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+alpha),cos(x+alpha),a+xsinalpha),(sin(x+beta),cos(x+beta),b+xsinbeta),(sin(x+gamma),cos(x+gamma),c+xsingamma):}| is independent of x .

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If D1=|[1, 1, 1],[x^2,y^2,z^2],[x, y, z]| and D2=|[1, 1, 1],[yz, zx,xy...

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  2. Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2...

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  3. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

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  4. If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

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  5. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

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  6. If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

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  7. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

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  8. Using the factor theorem it is found that a+b , b+c and c+a are thr...

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  9. Let |x^2+3xx-1x+3x+1-2xx-4x-3x+4 3x|=a x^4+b x^3+c x^2+e be an identi...

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  10. If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

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  11. If Delta1=|(1, 1 ,1),(a, b, c ),(a^2,b^2,c^2)|,Delta2=|(1,b c, a),(1,c...

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  12. The value of the determinant |a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n...

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  13. Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,si...

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  14. Evaluate: (i) |(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)|

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  15. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by expanding it along th...

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  16. Evaluate the determinant D=|[2 ,3,-2],[ 1, 2 ,3],[-2, 1,-3]| by expa...

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  17. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]|

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  18. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by method.

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  19. For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singul...

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  20. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

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