Math Problem Statement
Find the dimensions of the given matrix. A =
3 9 1 1/4
; a13 ✕ Identify the given entry. a13 =
Solution
The matrix is presented as:
3 & 9 & 1 \\ \frac{1}{4} \end{pmatrix}$$ ### Step 1: Determine the dimensions of matrix $$A$$ Matrix dimensions are given by the number of rows and columns. From the matrix: - The first row contains three elements: $$3$$, $$9$$, and $$1$$. - The second row contains only one element: $$\frac{1}{4}$$. Thus, matrix $$A$$ has 2 rows but the second row has fewer elements than the first, which indicates that it may not be a valid matrix, as matrices must have the same number of elements in each row. However, if we assume that the second row should have more elements (and the matrix is incomplete or poorly formatted), we cannot determine a valid size until we know all the values in the second row. ### Step 2: Identify the entry $$a_{13}$$ The notation $$a_{13}$$ refers to the element in row 1, column 3. From the matrix given: - Row 1, column 3 contains the element $$1$$. Thus, $$a_{13} = 1$$. Let me know if you'd like more details or have any questions! Here are 5 questions to expand on this topic: 1. What are the rules for determining valid matrix dimensions? 2. How can we handle incomplete or improperly formatted matrices? 3. What is the significance of matrix entries in linear algebra? 4. How do you perform matrix operations (like addition or multiplication)? 5. What is the difference between row vectors and column vectors? **Tip:** When reading matrix entries, always remember that the first index refers to the row, and the second refers to the column.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Dimensions
Matrix Notation
Formulas
Matrix dimensions = Rows × Columns
a_{ij} represents the element in the ith row and jth column
Theorems
Matrix Validity Theorem (matrices must have the same number of elements in each row)
Suitable Grade Level
Grades 9-12