Select the range D8:D9 and keep it selected then type =MMULT(A8:B9,D4:D5) … CSE … if it doesn’t work … check your typing …
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If it still doesn’t work, download my example file!įor the MMULT() array function, do the following:
And you should get the inverse matrix that you see in the range A8:B9 … it if doesn’t work, do it again carefully and if it still doesn’t work, check your typing. Select the range A8:B9 and keep it selected then type =MINVERSE(A4:B5) then press Control and keep it pressed, press Shift and keep it pressed as well then press Enter, now let go of all three keys I will call this CSE from now on!). So for the MIVERSE() function entry you must do the following: The following screenshot shows you my formulas … again, just copy them as you see them here but remember, array functions are not ordinary functions. The range A12:D13 contains the Proof area in which we test the solution that x = 5 and y = 1. The range A8:E9 includes the solution using firstly the MINVERSE() array function and then the MMULT() array function. All you do is type in, hard code, the entries in the range A3:D5 in this example. This is a two variable set of simultaneous equations and I have left column C blank to allow us to develop three variable examples. SOLVER solution: using the SOLVER add in to provide the values for the variables. The names indirect and direct are my own and I am classifying them as different methods although in reality they are not! this is essentially a single cell solution per variable. Indirect Method: Using the two array functions MINVERSE() and then MMULT() separately: this is essentially an entire problem or matrix solution that gives us the values of each variableĭirect Method Using the two array functions MINVERSE() and then MMULT() together in the form =MMULT(MINVERSE()). I am going to use three methods for solving simultaneous equations: Try it yourself for equation (2) if you wish. In this case I know that x = 5 and y = 1 and we an prove that by putting 5 where x is and 1 where 1 is in either of the two equations, such as in equation (1): For example, here are two simultaneous equations: Simultaneous equations get their name from the fact that in two or three or more equations, X has the same value for each, Y has the same value for each and so on.
If you know SEs you know there are several ways of solving them and I am not a mathematician so I am not going to explain Cramer’s rule, matrix algebra or even substitution … just show you how Excel can help. I remember, however, realising what they were and how they worked years after leaving school and then I thought, why on earth does anyone have a problem with them.
Simultaneous equations are usually a nightmare for the average secondary school student: they cannot or will not do them.
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