Examples of square, row, column, and zero matrices explained

📚 Quick Study Guide

• 🔢 A square matrix has the same number of rows and columns (e.g., 2x2, 3x3).
• ➡️ A row matrix has only one row (e.g., 1x3, 1x5).
• ⬇️ A column matrix has only one column (e.g., 3x1, 5x1).
• 0️⃣ A zero matrix is a matrix where all elements are zero.
• 📐 The order of a matrix is written as rows x columns (m x n).
• ➕ Matrices can only be added or subtracted if they have the same order.
• ➗ Scalar multiplication involves multiplying each element of a matrix by a constant.

Practice Quiz

1. Which of the following matrices is a square matrix?
   1. A) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}$
   2. B) $\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$
   3. C) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
   4. D) $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$
2. Which of the following matrices is a row matrix?
   1. A) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
   2. B) $\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$
   3. C) $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$
   4. D) $\begin{bmatrix} 1 & 2 \\ 0 & 0 \end{bmatrix}$
3. Which of the following matrices is a column matrix?
   1. A) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
   2. B) $\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$
   3. C) $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$
   4. D) $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
4. Which of the following matrices is a zero matrix?
   1. A) $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
   2. B) $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$
   3. C) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
   4. D) $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$
5. What is the order of the following matrix? $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$
   1. A) 3x2
   2. B) 2x3
   3. C) 3x3
   4. D) 2x2
6. If A = $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and B = $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$, what is A + B?
   1. A) $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$
   2. B) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
   3. C) $\begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix}$
   4. D) $\begin{bmatrix} 4 & 3 \\ 2 & 1 \end{bmatrix}$
7. If A = $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, what is 2A?
   1. A) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
   2. B) $\begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix}$
   3. C) $\begin{bmatrix} 3 & 4 \\ 5 & 6 \end{bmatrix}$
   4. D) $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$