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Evaluate : |(cos theta, sin theta),(-s...

Evaluate :
`|(cos theta, sin theta),(-sin theta,cos theta)|`

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NCERT TAMIL-MATRICES AND DETERMINANTS -EXERCISE 7.5
  1. Evaluate : |(cos theta, sin theta),(-sin theta,cos theta)|

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  2. If a(ij)=1/2 (3i-2j) and A= [a(ij)](2xx2) is

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  3. What must be the matrix X, if 2X+[(1,2),(3,4)]=[(3,8),(7,2)] ?

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  4. Which one of the following is not true about the matrix [(1,0,0),(0,0,...

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  5. If A and B are two matrices such that A + B and AB are both defined, t...

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  6. If A = [(lamda ,1 ),(-1,-lamda)] then for what value of lamda, A^2 = O...

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  7. If A= [(1,-1),(2,-1)] , B =[(a,1),(b,-1)] and (A+B)^2 =A^2 +B^2 then t...

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  8. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying the equation "...

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  9. If A is a square matrix, then which of the following is not symmetric?

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  10. If A and B are symmetric matrices of order n, where (A ne B), then

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  11. If A=[(a,x),(y,a)] and if xy = 1 then det ("A A"^T) is equal to

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  12. The value of x, for which the matrix A=[(e^(x-2),e^(7+x)),(e^(2+x),e^(...

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  13. If the points (x,−2), (5, 2), (8,8) are collinear, then x is equal to

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  14. If |(2a,x1, y1),(2b,x2,y2),(2c,x3,y3)|=(abc)/2 ne 0 , then the area o...

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  15. If the square of the matrix [(alpha,beta),(gamma,-alpha)] is the unit ...

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  16. If Delta=|(a,b,c),(x,y,z),(p,q,r)|, then |(ka,kb,kc),(kx,ky,kz),(kp,kq...

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  17. A root of the equation |(3-x,6,3),(-6,3-x,3),(3,3,-6-x)|=0 is

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  18. The value of the determinant of A=[(0,a,-b),(-a,0,c),(b,-c,0)] is

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  19. If x1 , x2 , x3 as well as y1 , y2 , y3 are in geometric progressio...

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  20. If lfloor.rfloor denotes the greatest integer less than or equal to t...

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  21. If a ne b , b ,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 then abc =

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