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Evaluate Delta=|0sinalpha-cosalpha-sinal...

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

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To evaluate the determinant \[ \Delta = \begin{vmatrix} 0 & \sin \alpha \\ -\cos \alpha & -\sin \alpha \\ \sin \beta & \cos \alpha \\ -\sin \beta & 0 ...
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Assertion : The system of linear equations x+(sinalpha)y+(cosalpha)z=0x+(cosalpha)y+(sinalpha)z=0x-(sinalpha)y-(cos\ alpha)z=0 has a non-trivial solution for only value of alpha lying the interval (0,\ pi) Reason: The equation in\ alpha cosalphas in alpha cosalphasinalpha cosalphasinalphac osalpha-sinalpha-cosalpha|=0 has only one solution lying in the interval (-pi/4,\ pi/4)

NCERT ENGLISH-DETERMINANTS-All Questions
  1. Evaluate |(x, x+1),(x-1,x)|

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

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  3. Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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  4. Find minors and cofactors of the elements of the determinant|2-3 5 6 ...

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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. Examine the consistency of the system of equations x + 2 y = 2" "2x +...

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  9. Solve system of linear equations, using matrix method, 5x + 2y = 4," ...

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  10. Examine the consistency of the system of equations 5x -y + 4z = 5," "...

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  11. Examine the consistency of the system of equations 3x -y - 2z = 2" "2...

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  12. Examine the consistency of the system of equations x + y + z = 1 2x + ...

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  13. If A is an invertible matrix of order 2, then det (A^(-1))is equal to...

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  14. Find the inverse the matrix (if it exists)given in[(1, 0, 0),( 0,cosal...

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  15. Find area of the triangle with vertices at the point given in each of...

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  16. Show that pointsA (a , b + c), B (b , c + a), C (c , a + b)are collin...

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  17. If A=|[3, 2], [7, 5]| and B=|[6 ,7], [8, 9]| , verify that (A B)^(-1)=...

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  18. Let A be a non-singular square matrix of order 3 xx3. Then |adj A| is ...

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  19. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

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  20. Let A=[[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], where ...

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