If a matrix is symmetric, what property does it have?
Practice Questions
Q1
If a matrix is symmetric, what property does it have?
A = A^T
A = -A
A^2 = I
A = 0
Questions & Step-by-Step Solutions
If a matrix is symmetric, what property does it have?
Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Learn about the transpose of a matrix. The transpose of a matrix is formed by flipping it over its diagonal, which means rows become columns and columns become rows.
Step 3: Know the definition of a symmetric matrix. A matrix is symmetric if it is equal to its transpose.
Step 4: Write the property of a symmetric matrix. This can be expressed as A = A^T, where A is the matrix and A^T is its transpose.
Step 5: Conclude that if a matrix is symmetric, it has the property that its elements are mirrored across the diagonal.
Symmetric Matrix – A matrix that is equal to its transpose, meaning A = A^T.
