In order to properly use MMULT, it’s important to understand how matrix multiplication works.  You can multiply any two matrices together as long as the number of columns in the first matrix is equal to the number of rows in the second matrix.  The size of the resulting matrix is determined by the input matrices.  If your matrix 1 has A rows and B columns, matrix 2 must have B rows, but could have any number, C, columns.  The resulting matrix would be A rows by C columns.

Assuming you’ve got a handle on matrix multiplication, the format for the MMULT function is:

=MMULT(array1, array2)

The way that you enter the function depends on what your result is going to be.  If your result is going to be a single value (meaning you have a 1xB array to multiply by a Bx1 array), you can simply enter the equation as above in a single cell.  However if your result will have multiple rows and/or columns, you should select the proper number of cells, type the function and then press SHIFT, CTRL, and ENTER together.  See below for some examples of using the MMULT function.

In cell B6: =MMULT(A1:B1,D1:D2) = 6

In cell B8: =MMULT(A3:B3,E1:E2) = 21

In cells D5:E6: =MMULT(A1:B2,D1:E2) then press SHIFT, CTRL, and ENTER

In cells G5:H7: =MMULT(A1:B3,D1:E2) then press SHIFT, CTRL, and ENTER

=DAVERAGE(range, field, criteria)

The range is the group of cells which you want to analyze and apply your criteria against.

The field is the column which you want to use in calculating the average.  You can input either the column number in your range or the actual name of the column in quotation marks.

The criteria is the range of cells containing the criteria which you want to use in calculating the average.

See below for examples of using the DAverage function on the sample database shown.  The database is in cells A4:E11, while the criteria are reflected in rows A and B.  Note that the column names in the criteria match the names in the database.  It isn’t necessary to have values entered in all of the criteria cells, only those that you’re interested in using.

=DAVERAGE(A4:E11,4,B1:B2) results in a value of 7.333 (the average of 11, 3, and 8 )

=DAVERAGE(A4:E11,4,B1:C2) results in a value of 5.5 (the average of 3 and 8 )

=DAVERAGE(A4:E11,”Units Sold”,C1:C2) results in a value of 7 (the average of 10, 7, 3, and 8 )

=DAVERAGE(A4:E11,5,B1:C2) results in a value of 46.5 (the average of 21 and 72 )

The SUMPRODUCT function in Excel is a useful tool when you are working with large datasets or multiple arrays.  An array is simply a series of numbers.  SUMPRODUCT takes two or more equally-sized arrays, multiplies the respective values, and adds the results.  The format for the function is =SUMPRODUCT (Array1, Array2, Array3,…).  So, if you were to think about two arrays: {1,2,3} and {5,4,6}, the SUMPRODUCT function would calculate 1*5 + 2*4 +3*6 = 31.  This function can save you a lot of time in your calculations, because you would normally have to perform each multiplication individually and then have another function to sum the products.  Now you can do it all in one step.  For some examples of the SUMPRODUCT function in action, consider the sample data and the corresponding results :

SUMPRODUCT (A2:A5,B2:B5) = 82

SUMPRODUCT (B2:B5,C2:C5) = 6

SUMPRODUCT (A2:A5,B2:B5,C2:C5) = 28

The values in Column C show an example of another way to use the SUMPRODUCT function: to perform computations based on logical TRUE/FALSE values.  If you have an equation set up where when conditions are TRUE = 1 and FALSE = 0, then you could use a SUMPRODUCT function with the 1’s and 0’s as one of your arrays to sum only the values where the condition is true.  Since the values corresponding to false are multiplied by 0, they don’t contribute to the result.  In the data above, if you were interested in only adding the values in Column B which were multiples of 2, you could write an IF statement to create the values in Column C corresponding to 1 when TRUE and 0 when FALSE, then use the SUMPRODUCT function to get your result of 6.

To begin, let’s take a look at the syntax below.

And( condition1, condition2, … )  : The condition is what we would like Excel to determine True or False. 

Take a look at the example below.

10 =AND(A1>1, A1<20)  : True

Ohio State  =AND(A1=30, A2=”Michigan”) : False

 Let’s go over the syntax.

 Char( ascii_value ) – The ascii_value is used to retrieve the character.

ASCII stands for American Standard Code for Information Interchange.  Below is an ASCII Table.

 Wikipedia Definition: In mathematics, the absolute value (or modulus) |a| of a real number a is a’s numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and ?3.

 Here an example of the Syntax.

 =ABS(number)    -  number refers to the numeric value in a specific cell

-45 will return 45
-0.235 will return .235
-0.1857 will return .1857
-143,765 will return 143,765

=FV(Interest Rate, Number of Payments, Payment Amount, Present Value, Type)

The Interest Rate is the interest rate earned on the investment per period.  The period is how often the investment payments are made.  For example, if the annual interest rate is 6.0% and you invest once a month, the interest rate you would enter is 6.0%/12, or 0.5%.  If the payments are only once a year then the interest rate you would enter would just be 6.0%.

The Number of Payments is the total number of investment payments made.  For example, weekly payments for 2 years would be 52*2 = 104 payments.  Annual payments for 25 years would be 25.

The Payment Amount is the amount of each investment payment.  Because Excel uses basic financial accounting principles, an investment would be entered as a negative value.  A positive value would correspond to an amount being borrowed.

The Present Value is an optional field, corresponding to the initial payment, if any, that is made.  So, if you were investing $500 initially and then $100 per month, the PV would be -500, and the Payment Amount would be -100.  If no value is interested for the Present Value, it is assumed to be 0.

The Type is another optional field, indicating whether the payments are made at the beginning or the end of the payment period.  Entering 1 for the Type value indicates payments made at the beginning of the period, while a 0 indicates payments made at the end of each period.  Payments at the end of the period is the default.

Below are some examples of FV equations and their results.  Typically, the values are entered into cells in Excel instead of into the equation itself.  This allows them to be easily changed to see how they impact the FV.

Investing $200 a month for 2 years at an interest rate of 7% = FV(7%/12,24,-200) => $5,136.21

Investing $100 now and $25 a week for 4 years at an interest rate of 5% = FV(5%/52,208,-25,-100) => $5,875.55

Investing $1000 at the beginning of each year for 40 years at an interest rate of 6% =FV(6%,40,-1000,0,1) => $164,047.68

=DAYS360(start date, end date, method)

The start date is the first date that you want to use, and the end date is the second.  Basically, the function takes (end date – start date) and returns how many days there are in between.  It is possible to produce negative values if your start date is chronologically after your end date.  The method is an optional value.  If left blank, or you enter TRUE, it will base the result on the American calendar.  Entering FALSE uses the European method.  You can use a variety of date formats for this function.  Some example functions using the data shown and their results:

=DAYS360(A1,A2) => 81

=DAYS360(A1,A3,TRUE) => 94

=DAYS360(A4,A3) => -26

= DSUM (Range, Field, Criteria)

The example below shows a case where the DSUM function could be useful.  The range that you’re interested in summing is contained in cells A4:E10.  The criteria are in cells A1:E2.  Whatever criteria you are using should have the same names as the columns in your range.  You only need to have values for the criteria which you want to use.  In this example, Order Number is left blank because it will not be used as a criterion.    The field is the column which you want to sum.  It can be either the number of the column in the range or the name of the column.  These examples show a variety of ways to use the DSUM function and the resulting values:

=DSUM(A4:E10,3,B1:B2) => 33

=DSUM(A4:E10,”Quantity”,B1:B2) => 33

=DSUM(A4:E10,5,B1:C2) => 89.25

=DSUM(A4:E10,5,B1:B2) => 106.75