How to Make a 3x3 Matrix in Excel

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Making a 3-by-3 matrix in Microsoft Excel is in fact very simple. You need only write numbers in each cell of any 3-by-3 block of cells. What has led to so much confusion regarding matrices in Excel is their functionality. A 3-by-3 matrix by itself provides no use unless you can either multiply it by another matrix, find its inverse or use it to solve a system of equations -- all three of which are possible in Excel.

Multiply Two Matrices

  • Type two matrices in 3-by-3 cell blocks anywhere on the sheet. The matrices need not be adjacent.

  • Highlight an empty 3-by-3 block of cells and press the "F2" key.

  • Press the "=" key on your keyboard and type "MMULT(."

  • Highlight all the cells containing the first matrix; type a comma and highlight all the cells containing the second matrix. Type ")."

  • Press and hold down the "Ctrl" and "Shift" keys, and then press the "Enter" key to finalize the calculation and make the resulting product matrix appear in the 3-by-3 block of cells you highlighted.

Find Matrix Inverse

  • Enter numbers in any 3-by-3 cell block. No more than one row may contain cells in which the numbers are the same.

  • Highlight an empty 3-by-3 block of cells and press the "F2" key.

  • Press the "=" key on your keyboard and type "MINVERSE(."

  • Highlight all the cells containing the original matrix and type ")."

  • Press and hold down the "Ctrl" and "Shift" keys, and then press the "Enter" key to make the inverse of the initial matrix appear in the empty 3-by-3 block of cells.

Solve System of Equations

  • Write the equations in the system of equations you're trying to solve in the form of x + y + z = c. You can write it on a piece of paper or in your computer's notepad. You need the coefficients to build the required matrices. This is an example:
    x + y + z = 10
    2x + 2y + 2z = 20
    3x + 3y + 3z = 30

  • Fill a 3-by-1 cell block with the numbers to the right of the equation: 10, 20 and 30.

  • Setup a 3-by-3 cell block matrix by using the coefficients to the left of the equation. Type
    1, 1 and 1 in the first row; 2, 2 and 2 in the second; 3, 3 and 3 in the third.

  • Highlight an empty 3-by-1 block of cells and press the "F2" key.

  • Press the "=" key on your keyboard and type "MMULT(MINVERSE(."

  • Click all the cells in the 3-by-3 block. Type ")." Type a comma and highlight all the cells containing the 3-by-1 matrix. Type another closed bracket.

  • Press and hold down the "Ctrl" and "Shift" keys, and then press the "Enter" key to make the values for x, y and z appear in the 3-by-1 block of cells you selected.

Tips & Warnings

  • Highlight multiple cells by clicking the first cell, holding down the "Shift" key and clicking the last cell.

References

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