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Compute the following: i)[[a, b],[ -b...

Compute the following:
i)`[[a, b],[ -b, a]]+[[a, b],[ b , a]]`.
ii) `[[a^2+b^2 , b^2+c^2], [a^2+c^2 , a^2+b^2]]+[[2 a b , 2 b c],[ -2 a c, -2 a b]]`
iii) `[[-1 , 4 ,-6] ,[ 8, 5 , 16],[ 2 , 8 , 5]]+[[12, 7 ,6 ],[ 8, 0, 5],[ 3, 2, 4]]`
iv) `[[cos ^2 x ,. sin ^2 x],[ sin ^2 x , cos ^2 x]]+[[sin ^2 x, cos ^2 x ],[ cos ^2 x ,sin ^2 x]]`.

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V PUBLICATION-MATRICES-QUESTION BANK
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  2. Let A=[[2 , 4 ],[ 3, 2]], B=[[1, 3] ,[ -2 , 5]], C=[[-2 , 5 ],[ 3, ...

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  3. Compute the following: i)[[a, b],[ -b, a]]+[[a, b],[ b , a]]. i...

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  4. Compute the indicated products. i) [[a , b],[ -b , a]] [[a, -b],[ b...

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

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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=[[2/5, 3/5, 1]...

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  7. Simplify costheta[[costheta, sin theta],[-sintheta, costheta]]+sinthet...

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

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

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

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  11. Solve the equation for x, y, z and t, if 2[[x, z],[ y, t]]+3[[1, -...

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  12. If x[[2],[3]]+y[[-1],[1]]=[[10],[5]] find the values of x and y.

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  13. Given 3[[x,y],[z,w]]=[[x,6],[-1,2w]]+[[4, x+y],[z+w, 3]] find the va...

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

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  15. Show that i) [[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[2 , 1 ],[3 ,...

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  16. Find A^2-5 A+6 I, if A=[[2, 0, 1],[ 2 ,1 , 3],[ 1, -1, 0]]

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  17. If A=[[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]], prove that A^3-6 A^2+7...

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  18. If A=[[3,-2],[4,-2]] and I=[[1,0],[0,1]], find k so that A^2=kA-2I

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  19. If A=[[0, -tan (alpha/2)], [ tan (alpha/2), 0]] and I is the identi...

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  20. A trust fund has Rs. 30,000 that must be invested in two different typ...

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