High School Pre-Calculus determinant of 2x2 matrix review questions

📚 Quick Study Guide

• 🔢 The determinant of a 2x2 matrix is a single number that can be calculated from the elements of the matrix.
• 📝 Given a 2x2 matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, the determinant is calculated as: $ad - bc$.
• ➕ The determinant is used in various applications, including solving systems of linear equations and finding the area of a parallelogram formed by the vectors represented by the rows (or columns) of the matrix.
• 💡 A determinant of zero indicates that the matrix is singular (non-invertible).
• 📐 Geometrically, the absolute value of the determinant represents the scaling factor of the linear transformation described by the matrix.

Practice Quiz

1. What is the determinant of the matrix $\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$?
   1. -2
   2. 5
   3. 11
   4. 14
2. Calculate the determinant of the matrix $\begin{bmatrix} -1 & 2 \\ 0 & 5 \end{bmatrix}$.
   1. -5
   2. 5
   3. 2
   4. -2
3. Find the determinant of the matrix $\begin{bmatrix} 3 & -2 \\ 1 & 1 \end{bmatrix}$.
   1. 1
   2. 5
   3. -1
   4. -5
4. What is the determinant of the matrix $\begin{bmatrix} 4 & 0 \\ 0 & 4 \end{bmatrix}$?
   1. 0
   2. 4
   3. 8
   4. 16
5. Compute the determinant of the matrix $\begin{bmatrix} -2 & -3 \\ -4 & -5 \end{bmatrix}$.
   1. -2
   2. 2
   3. -22
   4. 22
6. Determine the determinant of the matrix $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$.
   1. -1
   2. 0
   3. 1
   4. 2
7. Evaluate the determinant of the matrix $\begin{bmatrix} 1/2 & 1 \\ 0 & 1/2 \end{bmatrix}$.
   1. 0
   2. 1/4
   3. 1
   4. -1/4