Math Problem Statement
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What is the type and classification of the given matrices?
Solution
Let's go over the questions from the image.
Question 1:
The matrix shown is:
1 & 3 & 4 \\ 9 & 0 & 0 \end{pmatrix}$$ This matrix has **2 rows** and **3 columns**, which makes it a **2 × 3 matrix**. Therefore, the correct answer is: - **2 × 3 matrix** ### Question 2: The matrix shown is: $$\begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 8 \end{pmatrix}$$ This matrix has non-zero values only on the diagonal, and all other elements are zero. This satisfies the definition of a **diagonal matrix**, where all off-diagonal elements are zero. It is also a **square matrix** (3 rows and 3 columns), but since the primary focus is on the zero off-diagonal elements, the best classification is **diagonal matrix**. The selected option for this question is correct: - **Diagonal matrix** Let me know if you need any more details or clarifications! ### Relative Questions: 1. What are the properties of a **triangular matrix**? 2. How does a **zero matrix** differ from a **diagonal matrix**? 3. Can a matrix be both **diagonal** and **identity**? 4. What is the difference between a **square matrix** and a **rectangular matrix**? 5. How can you determine the **rank** of a matrix? ### Tip: For matrices, understanding their dimensions (rows × columns) is crucial in defining their type and determining possible operations like multiplication.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Dimensions
Matrix Types
Diagonal Matrix
Formulas
Matrix Dimensions: rows × columns
Diagonal Matrix Definition: non-zero elements only on the diagonal
Theorems
Basic Matrix Properties
Square Matrix Theorem
Suitable Grade Level
Grades 9-12