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

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],[1/5, 2/5, 4/5],[7/5, 6/5, 2/5]]` then compute 3A-5B

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`3A=[[2,3,5],[1,2,4],[7,6,2]]`, 5B=`[[2,3,5],[1,2,4],[7,6,2]]`
3A-5B=`[[0,0,0],[0,0,0],[0,0,0]]`
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A N EXCEL PUBLICATION-MATRICES-QUESTION BANK
  1. Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,...

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

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

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

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

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

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

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

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

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

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  12. If f(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0,0,1]] Find f(-x)

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  13. Show that [[5,-1],[6,7]] [[2,1],[3,4]] ne [[2,1],[3,4]] [[5,-1],...

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  14. Show that [[1,2,3],[0,1,0],[1,1,0]] [[-1,1,0],[0,-1,1],[2,3,4]] ne [...

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

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  16. Consider the matrices A=[[2,3],[4,5]] Prove thatA^2-7A-2I=0

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

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

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

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

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