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Show that costheta.[{:(costheta,sintheta...

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

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

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

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

If A = ((costheta,-sintheta),(sintheta,costheta)) then

Evaluate : |{:(costheta,-sintheta),(sintheta,costheta):}|

costheta[(costheta, sintheta),(-sintheta,costheta)]+sintheta[(sintheta,-costheta),(costheta,sintheta)] is equal to (A) [(0,0),(1,1)] (B) [(1,1),(0,0)] (C) [(0,1),(1,0)] (D) [(1,0),(0,1)]

Simplify costheta[costhetasinthetasinthetacostheta]+sintheta[sintheta-costhetacosthetasintheta]

Evaluate Delta=|{:(sintheta, costheta),(-costheta,sintheta):}|

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Evaluate costheta.costheta+sintheta.sintheta

RS AGGARWAL-MATRICES-Exercise 5F
  1. Construct a 2xx3 matrix whose elements are given by a(ij)=(1)/(2)|-3...

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  2. If [{:(x+2y,-y),(3x,4):}]=[{:(-4,3),(6,4):}], find the values of x and...

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  3. Find the values of x and y, if 2[{:(1,3),(0,x):}]+[{:(y,0),(1,2) :}]...

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  4. If x.[{:(2),(3):}]+y.[{:(-1),(1):}]=[{:(10),(5):}], find the values of...

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  5. If [{:(x,3x-y),(2x+z,3y-w):}]=[{:(3,2),(4,7):}], find the values of w...

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  6. If [{:(x,6),(-1,2w):}]+[{:(" "4,x+y),(z+w," "3):}]=3[{:(x,y),(z,w):}],...

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  7. If A=" diag "(3" "-2" "5)" and "B=" diag "(1" "3" "-4)," find "(A+B).

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  8. Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sint...

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  9. If A=[{:(1,-5),(-3," "2),(4,-2):}]" and "B=[{:(3," "1),(2,-1),(-2," "3...

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  10. If A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}], then find the lea...

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  11. Find the values of x and y for which [{:(2,-3),(1," "1):}][{:(x),(y)...

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  12. Find the values of x and y for which [{:(x,y),(3y,x):}][{:(1),(2):}]...

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  13. If A=[{:(4,5),(1,8):}], show that (A+A') is symmetric.

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  14. If A=[{:(2,3),(4,5):}], show that (A-A') is skew-symmetric.

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  15. If A=[{:(2,-3),(4," "5):}]" and "B=[{:(-1,2),(0,3):}], find a matrix X...

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  16. If A=[{:(4,2),(1,3):}]" and "B=[{:(-2,1),(3,2):}], find a matrix X suc...

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  17. If (i) A=[cosalphasinalpha-sinalphacosalpha] , then verify that Aprime...

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  18. If A and B are two symmetric matrix of same order, then show that (AB-...

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  19. If f(x)=x^2-4x+1 then find f(A) when A=[[2,3] , [1,2]]

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  20. A matrix which is both symmetric as well as skew-symmetric is a

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