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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 .

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

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  2. A particle just clears a wall of height b at distance a and strikes...

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

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  4. If y=sinm x , then the value of the determinant |y y1y2y3y4y5y6y7y8|,w...

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  5. Find the value of the determinant |[1, 1, 1, 1],[ 1, 2, 3, 4],[ 1, 3, ...

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  6. The parameter on which the value of the determinant |[1,a...

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  7. If x=c y+b z ,y=a z+c x ,z=x+a y ,w h e r e .x ,y ,z are not all zer...

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  8. If |[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^...

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  9. The value of |-1 2 1 3+2sqrt(2) 2+2sqrt(2) 1 3-2sqrt(2...

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  10. Find the following system of equations is consistent, (a+1)^3x+(a+2...

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  11. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

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  12. If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are...

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  13. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

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  14. The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a.|b x+a ...

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  15. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

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  16. Prove that |{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)...

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  17. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

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  18. Factorize the following |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^4+...

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  19. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

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  20. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

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