If a matrix is symmetric, what can be said about its elements? (2021)
Practice Questions
1 question
Q1
If a matrix is symmetric, what can be said about its elements? (2021)
Aij = Aji
Aij = -Aji
Aij = 0
Aij = Aii
A symmetric matrix satisfies the condition Aij = Aji for all i and j.
Questions & Step-by-step Solutions
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Q
Q: If a matrix is symmetric, what can be said about its elements? (2021)
Solution: A symmetric matrix satisfies the condition Aij = Aji for all i and j.
Steps: 5
Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Learn what a symmetric matrix is. A symmetric matrix is a square matrix that is equal to its transpose.
Step 3: Know what transpose means. The transpose of a matrix is formed by flipping it over its diagonal, which means rows become columns and columns become rows.
Step 4: Identify the condition for symmetry. For a matrix to be symmetric, the element in the ith row and jth column (Aij) must be equal to the element in the jth row and ith column (Aji).
Step 5: Apply the condition. This means that if you look at any element in the matrix, it should be the same as its corresponding element on the opposite side of the diagonal.
