### How To - Determinants of Matrices

The

There are three basic cases for matrices, dimensions

Results for the three exercises will be posted at the end.

In the case of matrix

For example

**determinant**of a matrix is very useful and commonly asked for in exams. With it, you can determine if a matrix is invertible (thus find the inverse for sure, without wasting tons of precious time in an exam) and it's a sure way to get points even if you are pretty hopeless and just want to passThere are three basic cases for matrices, dimensions

**2x2**,**3x3**and dimensions**3<**.Results for the three exercises will be posted at the end.

**Tipp**: a matrix can only be inverted if the determinant**does not**equal**0**!In the case of matrix

**A**(2x2) the main- minus minor-diagonal formula applies; with upper left times lower right, minus upper right times lower left.For example

**B**(3x3) it becomes more complicated. We can apply the**rule of Sarrus**(Wikipedia). For that, we replicate the first two columns to the right side. Now we create the main and minor diagonals, as seen in the picture below:
After this, we subtract the sum of the minors from the sum of the main diagonals and receive the determinant :)

Example

**C**is a lot more work, but usually asked for in exams as it is basically includes the rule of Sarrus.
Try to pick the

**column or row with the most zeros**or ones, in this case we of course choose the third row.
Starting with

**1. we cancel out the first column**, and create a 3x3 matrix out of the remaining 9 numbers.
Then we do the same with

**2. this time for the second column**and so on for 3. and 4.
We will be needing the determinants for each of these matrices and multiply them with the factor, which is the digit 1 to 4 of the third row.

The

**determinants which are multiplied with factor 0 can just be canceled out**- now you see why we picked the row with the most zeros :D
Solutions: det(A) = -7; det(B) = -5; det(C) = 60

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