Math Problem Statement
Find the dimensions of the given matrix.
D =
17
−19
5
0
−5
4
50
19
;
d31
✕
Identify the given entry.
d31 =
Solution
Step 1: Identify the Dimensions of the Matrix
The given matrix is written in a compressed form. Expanding it:
\begin{bmatrix} 17 & -19 & 5 \\ 0 & -5 & 4 \\ 50 & 19 & d_{31} \end{bmatrix}$$ The matrix has: - **Rows:** 3 (as there are 3 horizontal levels of elements). - **Columns:** 3 (as there are 3 vertical levels of elements in each row). Thus, the dimensions of $$D$$ are **$$3 \times 3$$**. --- ### Step 2: Identify the Entry $$d_{31}$$ The subscript $$d_{31}$$ specifies the **entry in the 3rd row and 1st column** of the matrix $$D$$. From the matrix: $$d_{31} = 50$$ --- ### Final Answer: 1. **Dimensions of the matrix $$D$$:** $$3 \times 3$$. 2. **Value of $$d_{31}$$:** $$50$$. Would you like additional details or further questions? Here are some extensions: 1. What are the properties of $$3 \times 3$$ matrices in linear algebra? 2. How can you determine if this matrix is invertible? 3. What does the determinant of this matrix represent? 4. How can $$d_{31}$$ affect computations like row reductions or determinants? 5. What is the significance of specific positions in matrices for matrix multiplication? **Tip:** Always label rows and columns clearly when working with matrix elements to avoid misidentification!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Algebra
Formulas
Matrix dimensions identification
Theorems
Matrix entry identification
Suitable Grade Level
Grades 9-12