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If A=[(costheta,sintheta),(-sintheta,cos...

If `A=[(costheta,sintheta),(-sintheta,costheta)]` Find `A^2`

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If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2=[[cos2theta,sin2theta],[-sin2theta,cos2theta]]

Simplify costheta[[costheta, sin theta],[-sintheta, costheta]]+sintheta[[sintheta, -costheta],[costheta, sintheta]]

Find dy/dx of x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta)

Solve sin2theta+costheta=0

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is independent of theta

The parametric representation of a point on the ellipse whose foci are (3,0) and (-1,0) and eccentricity 2//3 , is a) (1+3costheta,sqrt(3)sintheta) b) (1+3costheta,5sintheta) c) (1+3costheta,1+sqrt(5)sintheta) d) (1+3costheta,sqrt(5)sintheta)

If sintheta_(1)sintheta_(2)-costheta_(1)costheta_(2)+1=0 , then the value of tan(theta_(1)//2)cot(theta_(2)//2) is always equal to

Prove by mathematical induction. (costheta +i sintheta)^n=(cosntheta+isinntheta), where i=sqrt(-1)

Find dy/dx if x=a(theta-sintheta) , y=a(1-costheta)

BODY BOOKS PUBLICATION-MATRICES-EXERCISE
  1. Consider the matrix A=[(3,10),(2,7)] Find A^-1 using elementary row tr...

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  2. If A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]], prove that A^n=[[3^(n-...

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  3. If A=[(costheta,sintheta),(-sintheta,costheta)] Find A^2

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  4. If A=[[cos theta, sin theta],[ -sin theta, cos theta]], then prove ...

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  5. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  6. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  7. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  8. Write two non-zero matrices A and B for which AB=0.

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  9. Express A=[(1,-1),(2,3)] as the sum of a symmetric matrix and a skew s...

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  10. Let A=[a(ij)](2times3) where a(ij=i+j. construct A.

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  11. For any square matrix A,prove that A+A' is symmetric.

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  12. If A is a skew symmetric matrix of order 3. Then prove that it's deter...

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  13. Given abs [[2+x,3,4],[1,-1,2],[x,1,5]] is a singular matrix. Find the ...

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  14. Given A and B are square matrices of order 2 such that absA=-1, absB=3...

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  15. For the symmetric matrix A=[(2,x,4),(5,3,8),(4,y,9)].Find the value of...

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  16. If A=[(3,1),(-1,2)] . Show that A^2-5A+7I=0 Hence find A^4 and A^-1 ...

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  17. Using elementary row operations, find the inverse of the matrix [[1,...

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  18. Find x and y if x[[2],[3]]+y[[-1],[1]]=[[10],[5]]

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  19. Express the matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]] as the sum of a ...

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  20. The value of k such that matrix [[1,k],[-k,1]] is symmetric if

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