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Evaluate Delta=|[0,sinalpha,-cosalpha],[...

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

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To evaluate the determinant \[ \Delta = \begin{vmatrix} 0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0 \end{vmatrix} ...
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Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sinalpha,0,sinbeta],[cosalphas-sinbeta,0]|=0

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

Evaluate the following: |[cosalpha, sinalpha],[sinalpha, cosalpha]|

If A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] , then

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Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}]

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If /_\ = |[sinalpha, cosalpha, sin(alpha+delta)],[sinbeta, cosbeta, sin(beta+delta)],[singamma, cosgamma, sin(gamma+delta)]| then prove that /_\ is independent of alpha, beta, gamma and delta.

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costheta-sintheta=cosalpha-sinalpha

NCERT-DETERMINANTS-SOLVED EXAMPLES
  1. Evaluate |(x,x+1),(x-1,x)|

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  2. Find values of x for which abs((3,x),(x,1))=abs((3,2),(4,1))

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

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  4. Verify Property 2 for Delta=|[2,-3, 5],[ 6, 0, 4],[ 1, 5,-7]|

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  5. Verify Property 1 for Delta=|[2,-3, 5],[ 6, 0, 4],[ 1, 5,-7]|

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  6. Write the value of the following determinant: |[102, 18, 36],[ 1, 3, 4...

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  7. Evaluate Delta=|[3, 2, 3],[ 2, 2, 3], [3, 2, 3]|

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  8. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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  9. EvaluateDelta=|1a b c1b c a1c a b|

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  10. Show that |[a, b, c],[ a+2x, b+2y, c+2z],[ x, y ,z]|=0

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  11. Prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]...

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  12. Show that|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc(1+1/a+1/b+1/c)=abc+bc+ca+...

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  13. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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  14. Prove that |b+c a a b c+a b cc a+b|=4a b c

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  15. If x, y, z are different and Delta=|[x,x^2, 1+x^3],[y, y^2,1+y^3],[z, ...

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  16. Find the equation of the line joining A( 1,3) and B (0,0) using deter...

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  17. Find the minor of element 6 in the determinant Delta=|[1, 2, 3],[ 4, 5...

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  18. The sum of three numbers is 6. If we multiply third number by 3 and a...

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  19. Solve the following system of equations by matrix method. 3x-2y + 3z=...

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  20. Solve the system of equations 2x + 5y = 1 and 3x + 2y = 7.

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