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Simplify costheta[[costheta,sintheta],[s...

Simplify `costheta[[costheta,sintheta],[sintheta,costheta]]+sintheta[[sintheta,-costheta],[costheta,sintheta]]`

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Consider `costheta[[costheta,sintheta],[-sintheta,costheta]]+sintheta[[sintheta,-costheta],[costheta,sintheta]]`

`=[[ cos ^ 2 θ,sinθ.cosθ],[ −cosθ.sinθ, ​ ...
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Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

Simplify: costheta[costhetasintheta-sinthetacostheta]+sintheta[sintheta-costhetacosthetasintheta]

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta.[{:(sintheta,-costheta),(costheta,sintheta):}]=I.

Simplify the following : cos theta [{:(costheta,-sintheta ),(sintheta,costheta ):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]

costheta[{:(costheta,-sin theta),(sintheta,costheta):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]=?

If A=[[costheta,-sintheta],[sintheta,costheta]] then show that A^n = [[cosntheta,-sinntheta],[sinntheta,cosntheta]]

Statement 1: If A is an orthogonal matrix of order 2, then |A|=+-1. Statement 2: Every two-rowed real orthogonal matrix is of any one of the forms [[costheta ,-sintheta ],[sintheta ,costheta]]or[[costheta ,sintheta],[ sintheta,-costheta]]dot

(1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

(sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2cosectheta

NCERT ENGLISH-MATRICES-All Questions
  1. Using elementary transformations, find the inverse of the matrix[[2 ,...

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  2. Matrices A and B will be inverse of each other only if (A) A B=B A(...

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  3. Simplify costheta[[costheta,sintheta],[sintheta,costheta]]+sintheta[[s...

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  4. Find X and Y, if(i) X+Y=[[7, 0],[ 2, 5]]and X-Y=[[3, 0],[ 0 ,3]](ii) 2...

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  5. If A=[[1 ,2,-3],[ 5, 0, 2],[ 1,-1, 1]], B=[[3,-1, 2],[ 4, 2 ,5],[ 2, 0...

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  6. If A=[[2/3, 1, 5/3],[ 1/3, 2/3, 4/3] ,[7/3, 2, 2/3]]and B=[[2/3, 3/5, ...

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  7. Compute the following:(i) [[a, b],[-b, a]]+[[a, b],[b ,a]] (ii) [[a^2...

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  8. Compute the indicated products.(i) [[a, b],[-b ,a]][[a,-b],[b, a]] (ii...

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  9. Let A=[[2 ,4],[ 3 ,2]], B=[[1 ,3],[-2, 5]], C=[[-2, 5],[ 3, 4]]Find ea...

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  10. Find X, if Y=[[3, 2],[ 1, 4]]and 2X+Y=[[1 ,0],[-3, 2]]

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  11. Find x and y, if 2[[1, 3],[ 0,x]]+[[y,0], [1, 2]]=[[5, 6],[ 1, 8]]

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  12. Find the value of a, b, c and d from the equation:[[a-b,2a+c],[2a-b,3c...

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  13. Find the values of x, y and z from the following equations:(i) [[4, 3...

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  14. Construct a 3 xx 4matrix, whose elements are given by:(i) a(i j)=1/2|...

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  15. Construct a 2 xx2matrix, A =[a(i j)], whose elements are given by:(i) ...

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  16. If a matrix has 18 elements, what are the possible orders it can have...

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  17. If a matrix has 24 elements, what are the possible orders it can have...

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  18. In the matrix A=[[2,5,19,7],[35,-2,5/2,12],[sqrt3,1,-5,17]], write: (i...

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  19. Which of the given values of x and y make the following pair of matri...

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  20. A =([a(i j)])(mxxn)is a square matrix, if (a) m < n (b) m > n (c) m =...

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