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I have a matrix, a list of positions, and a vector.

I want a new matrix with the values of the vector inserted into the original matrix based upon the list of positions.

For example:

oldMatrix = {{a1, a2, a3, a4}, {b1, b2, b3, b4}, 
             {c1, c2, c3, c4}, {d1, d2, d3, d4}};

positions = {{1, 1}, {2, 3}, {3, 2}, {4, 1}}

newElements = {A1, B3, C2, D1}

Then I want the new matrix to be

Mathematica graphics

If I was working with a vector rather than a matrix this would be easy:

newVector                = oldVector
newVector[[{positions}]] = newElements

as vectors support a list when indexing.

This will not work with matrices.

I have searched and read with interest this answer but it doesn't fit this problem.

The best I have been able to come up with is:

setMatrix[matrix_, positionsMatrix_, vector_] := Module[
  {
   vectorF,
   positionsVector,
   row,
   column
   },

  vectorF = Flatten[matrix];
  {row, column} = Dimensions[matrix];

  positionsVector = Map[(#[[1]] - 1)*row + #[[2]] &,
    positionsMatrix];

  vectorF[[positionsVector]] = vector;

  Partition[vectorF, row]
  ]

but I would hope there was a simpler, more elegant and efficient approach.

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closed as off-topic by Bob Hanlon, ciao, kale, MarcoB, dr.blochwave Sep 13 '15 at 18:16

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, ciao, kale, MarcoB, dr.blochwave
If this question can be reworded to fit the rules in the help center, please edit the question.

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oldMatrix = {{a1, a2, a3, a4}, {b1, b2, b3, b4}, {c1, c2, c3, 
    c4}, {d1, d2, d3, d4}};

positions = {{1, 1}, {2, 3}, {3, 2}, {4, 1}};

newElements = {A1, B3, C2, D1};

(newMatrix = 
   ReplacePart[oldMatrix, 
    Thread[positions -> newElements]]) // MatrixForm

enter image description here

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