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Compute the following: [[a^2+b^2, b^2+...

Compute the following:
`[[a^2+b^2, b^2+c^2],[a^2+c^2, a^2+b^2]]+[[2ab, 2bc],[-2ac, -2ab]]`

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Given sum=`[[a^2+b^2+2ab, b^2+c^2+2bc],[a^2+c^2-2ac, a^2+b^2-2ab]]=[[(a+b)^2, (b+c)^2],[(a-c)^2, (a-b)^2]]`
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Using properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Prove that abs[[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]] =2abc(a+b+c)^3

Prove that |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^2

By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-2b],[2ab,1-a^2+b^2,2a],[2b ,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

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Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

If the product abc =1, then the value of the determinant |{:( -a ^(2), ab, ac),( ba, -b ^(2), bc),(ac, bc,-c ^(2)):}| is

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A N EXCEL PUBLICATION-MATRICES-QUESTION BANK
  1. Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each ...

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  2. Compute the following: [[a,b],[-b,a]]+[[a,b],[b,a]]

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  3. Compute the following: [[a^2+b^2, b^2+c^2],[a^2+c^2, a^2+b^2]]+[[2ab...

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  4. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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  5. Compute the following: [[cos^2x, sin^2x],[sin^2x, cos^2x]]+[[sin^2x,...

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  6. Compute the following: [[a,b],[-b,a]][[a,-b],[b,a]]

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  7. Compute the following: [1 \ 2 \ 3]+ [2 \ 3 \ 4]

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  8. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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  9. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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  10. Compute the following: [[2,1],[3,2],[-1,1]] [[1,0,1],[-1,2,1]]

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  11. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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  12. Let A=[[1,2],[3,4]] , B=[[2,1],[4,5]] , C=[[1,-1],[0,2]] Show that (...

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

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

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  16. Find X and Y if 2X+3Y=[[2,3],[4,0]] and 3X+2Y=[[-2,2],[-1,5]]

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

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

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  19. Solve the equation for x,y,z and t, if 2[[x,z],[y,t]]+3[[1,-1],[0,2]]=...

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

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