Math Problem Statement
Given the 4x4 matrix, what is the element located at (i = 1, j = 4)?
Solution
The image shows a matrix with four rows and four columns, with the notation and . This likely indicates that you are required to perform a specific operation or retrieve a specific element from the matrix based on the indices and .
Matrix:
1 & 8 & 2 & -3 \\ 3 & -2 & 0 & 4 \\ 5 & -3 & 7 & -1 \\ 3 & 2 & 0 & 2 \end{pmatrix}$$ ### For $$i = 1$$ and $$j = 4$$: - $$i$$ refers to the row number. - $$j$$ refers to the column number. So, you are looking for the element at the intersection of the 1st row and the 4th column, which is $$-3$$. Thus, the element at $$(i = 1, j = 4)$$ is $$-3$$. Would you like further details or additional questions related to this topic? Here are five possible follow-up questions: 1. How would you calculate the determinant of this 4x4 matrix? 2. What is the minor of the element located at $$(i = 1, j = 4)$$? 3. How can we find the cofactor of the element at $$(i = 1, j = 4)$$? 4. What is the inverse of this matrix, if it exists? 5. How do you perform Gaussian elimination on this matrix? ### Tip: To calculate the determinant of a 4x4 matrix, you can use cofactor expansion along any row or column for simplicity.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix
Linear Algebra
Formulas
Matrix indexing formula A(i,j)
Determinant of a matrix
Theorems
Matrix Element Identification
Suitable Grade Level
Grades 9-12