Matrix Inversion with Excel

While doing my homework 5 of Applied Colorimetry, I find it's pretty handy to do simple matrix calculation (inversion and multiplication) in Excel rather than coding in MATLAB. Following is the step-by-step procedure available on http://faculty.kfupm.edu. Enjoy!

Suppose you want to find the inverse of the matrix

And you want to use Excel to assist you in finding the inverse.  Well, Excel can do that for you.  However, you have to do certain things in order for Excel to do its job.  The first thing you need to do is to enter the matrix in the worksheet; entering the matrix in the worksheet is a matter of typing the numbers (elements) of the matrix, each element in a separate cell.  So, open up Excel and start entering the numbers as shown in the figure below:

Once you entered the elements of the matrix, you can invoke the MINVERSE function which computes the inverse of the matrix.  Before you invoke the function, you have to highlight an area of cells with equal number of rows and columns as the matrix you like to invert.  In the figure below, I highlighted an area of 3 rows and 3 columns:

Type the equal sign "=" before you click anywhere, like this:

Once you are done, click on "Insert Function" button on the left side of the Formula Bar:

Clicking on "Insert Function" button opens up the "Insert Function" dialog box:

From the "Or select a category:" menu right below and to the left of the "Go" button, choose "Math & Trig":

And from the "Select a function:" list, choose "MINVERSE":

Once you clink on "OK" button, the "Function Arguments" dialog box comes up:

Now go ahead and select the cells that contain the matrix you like to find the inverse of:

That last thing you have to do before you get the inverse of the matrix is to press and hold the ‘Ctrl’ and ‘Shift’ keys and then press the ‘Enter’ key.  Excel will now fill the area you selected to hold the inverse of the matrix with the inverse:

And that’s the end of it.

There are some shortcuts to all of this.  Assume that you want to find the inverse of another matrix, all what you have to do now is to select the proper size of cells, type "=", and from left upper corner below the standard toolbar, click on the name of the function you just used, in this case, it is "MINVERSE":

Matrix Multiplication with Excel

You want to multiply two matrices such as the matrix and a one-column matrix:

You know the result of the multiplication is a 3 ´ 1 matrix because the first matrix is 3 ´3 and the second matrix is 3´ 1. Excel can do the multiplication for you also. The first thing you have to do is to enter the elements the two matrices into the worksheet:

Now, go ahead and highlight an area of cells equal to the size of the matrix which is the result of the multiplication; in your case, you need to highlight 3 rows and one column:

Type the equal sign "=" before you click anywhere:

Now, go and click on "Insert Function" and choose from the "or select a category" menu "Math & Triq" category.   From the "Select a function" list, search for and choose "MMULT":

Click on "OK" button.  After that, the "Function Arguments" dialog box comes up:

In the "Array 1" field, enter the range of the first matrix by highlighting the cells that hold the matrix.  Then, click on the "Array 2" field and enter the range of the second matrix in the same way you did for the first field:

Press and hold the ‘Ctrl’ and ‘Shift’ keys and then press the ‘Enter’ key.  Excel will then give you the result of multiplying the two matrices:

You can use the shortcut as explained earlier to call the "MMULT" function.