# MDETERM Function in Excel

MDETERM Function in Microsoft Excel

### Part 1: Introduce

Definition:
The MDETERM function in Microsoft Excel returns the matrix determinant of an array.

Purpose:
Matrix determinants are generally used for solving mathematical equation systems involving several variables.

Syntax & Arguments:

syntax
`MDETERM(array)`

Explain the Arguments in the function:

• Array: Required. A numeric array with an equal number of rows and columns. This array can be given as a cell range (e.g., A1:C3), as an array constant (e.g., {1,2,3;4,5,6;7,8,9}), or as a name to either of these.

Return value:
The matrix determinant is a number derived from the values in the array.

Remarks:

• MDETERM returns the `#VALUE!` Error when:
• Any cells in the array are empty or contain text.
• The array does not have an equal number of rows and columns.
• MDETERM is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is incomplete.

### Part 2: Examples

🔹 Example 1:
Purpose of example: Determinant of a 3×3 matrix.
Data sheet and formulas:

ABC
1385
2361
3110
=MDETERM(A1:C3)Result88

Explanation:
This example calculates the determinant of a 3×3 matrix using the MDETERM function.

🔹 Example 2:
Purpose of example: Determinant of a matrix using array constants.
Data sheet and formulas:

ABC
1361
2110
33102
=MDETERM({3,6,1;1,1,0;3,10,2})Result1

Explanation:
This example demonstrates using array constants directly in the MDETERM function to calculate the determinant.

🔹 Example 3:
Purpose of example: Determinant of a 2×2 matrix using array constants.
Data sheet and formulas:

AB
136
211
=MDETERM({3,6;1,1})Result

Explanation:
This example calculates the determinant of a 2×2 matrix using array constants.

🔹 Example 4:
Purpose of example: Error due to unequal rows and columns.
Data sheet and formulas:

ABCD
11385
21361
=MDETERM({1,3,8,5;1,3,6,1})Result#VALUE!

Explanation:
This example returns an error because the array does not have an equal number of rows and columns.

🔹 Example 5:
Purpose of example: Determinant of a 4×4 matrix.
Data sheet and formulas:

ABCD
11385
21361
373102
=MDETERM(A1:D3)Result88

Explanation:
This example calculates the determinant of a 4×4 matrix using the MDETERM function.

🔹 Example 6: Using MDETERM with IF
Purpose of example: Determine if the matrix determinant is positive or negative.
Data sheet and formulas:

ABC
1253
2416
3732
=IF(MDETERM(A1:C3)>0, “Positive”, “Negative”)ResultPositive

Explanation:
This example checks if the determinant of the matrix is positive or negative using the IF function. If the determinant is positive, it returns “Positive”; otherwise, it returns “Negative”.

🔹 Example 7: Using MDETERM with SUM
Purpose of example: Sum the matrix determinant with another value.
Data sheet and formulas:

ABC
1324
2561
3873
=SUM(MDETERM(A1:C3), 10)Result52

Explanation:
This example calculates the determinant of the matrix and then adds 10 to the result using the SUM function.

🔹 Example 8: Using MDETERM with VLOOKUP
Purpose of example: Find the determinant value from a lookup table.
Data sheet and formulas:

ABCDEF
112345“Matrix A”
245660“Matrix B”
37890“Matrix C”
=VLOOKUP(MDETERM(A1:C3), E1:F3, 2, FALSE)ResultMatrix A

Explanation:
This example uses the VLOOKUP function to find the name of the matrix based on its determinant value from a lookup table.

🔹 Example 9: Using MDETERM with AVERAGE
Purpose of example: Average the matrix determinant with another set of numbers.
Data sheet and formulas:

ABC
1246
2853
3719
=AVERAGE(MDETERM(A1:C3), 5, 10, 15)Result8.75

Explanation:
This example calculates the average of the matrix determinant and three other numbers (5, 10, 15) using the AVERAGE function.

🔹 Example 10: Using MDETERM with MAX
Purpose of example: Find the maximum value between the matrix determinant and another set of numbers.
Data sheet and formulas:

ABC
1369
2258
3147
=MAX(MDETERM(A1:C3), 10, 20, 30)Result30

Explanation:
Using the MAX function, this example determines the maximum value between the matrix determinant and three other numbers (10, 20, 30).

🔹 Example 11: Using MDETERM with MIN
Purpose of example: Find the minimum value between the matrix determinant and another set of numbers.
Data sheet and formulas:

ABC
1135
2792
3468
=MIN(MDETERM(A1:C3), 5, 10, 15)Result5

Explanation:
Using the MIN function, this example determines the minimum value between the matrix determinant and three other numbers (5, 10, 15).

🔹 Example 12: Using MDETERM with ROUND
Purpose of example: Round the matrix determinant to the nearest whole number.
Data sheet and formulas:

ABC
1258
2369
3471
=ROUND(MDETERM(A1:C3), 0)Result27

Explanation:
This example rounds the determinant of the matrix to the nearest whole number using the ROUND function.

### Part 3: Tips and tricks

1. Ensure that the array you provide has an equal number of rows and columns to avoid the `#VALUE!` error.
2. You can use cell ranges, array constants, or names to provide the array to the MDETERM function.
3. Remember that the matrix determinant is a single number derived from the values in the array, and it’s used for solving systems of mathematical equations.