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## Determinants and Inverses of 2 x 2 Matrices

#### High School - HSN-VM.C.12

What are Determinants and Inverses of Matrices? The determinant is a scaler value of a squared matrix which encodes specific properties of the linear transformation. Finding the determinant value of a 2 x 2 matrix is, you can multiply the 1st and 3rd element and 2nd and 4th element. Now, you have to subtract the previous one with the latter one. In some cases you will be forced to expand from the third row. That means, we placed a pointer on each element of the row and neglected all elements above it and on its side(s). Not to mention that before the second element, the sign is minus. So, if the element has a minus sign of its own, then the signs will cancel each other out. The inverse of a matrix is basically a reciprocal or one over the value. When you multiply a matrix by its inverse we get an Identity Matrix. Students will learn how find and use determinants and inverses with matrices.

### Printable Worksheets And Lessons  #### Homework Sheets

Sheet 1 = Determinants, Sheet 2 and 3 = The Inverse of 2 x 2 Matrices.

• Homework 1 - Code breakers have used inverse matrices for years to help them decrypt messages.
• Homework 2 - We can express the inverse of a 2 x 2 matrix several ways, we show you one way.
• Homework 3 - An inverse matrix yields the identity matrix when multiplied by the original matrix.

#### Practice Worksheets

The practice sheets follow the same topic pattern as the practice sheets.

• Practice 1 - What is the inverse of the following matrices?
• Practice 2 - You can express the determinant of a 2 x 2 matrix as: l A l = ad - bc .
• Practice 3 - I wish I could have used this method in some physics applications.

#### Math Skill Quizzes

I used small numbers to make sure that they can focus on the concept, not the calculations.

• Quiz 1 - Determinants help us predict theoretical outcomes and results.
• Quiz 2 - The applications of this form of math is more geared toward theory.
• Quiz 3 - Now we will calculate by using this method.