If a matrix is said to be skew-symmetric, what must be true about its elements?
Practice Questions
Q1
If a matrix is said to be skew-symmetric, what must be true about its elements? (2023)
All elements are zero
a_ij = -a_ji
a_ij = a_ji
All diagonal elements are zero
Questions & Step-by-Step Solutions
If a matrix is said to be skew-symmetric, what must be true about its elements? (2023)
Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Learn what skew-symmetric means. A skew-symmetric matrix is a special type of matrix.
Step 3: Identify the condition for skew-symmetric matrices. For a matrix to be skew-symmetric, the element in the ith row and jth column (a_ij) must be the negative of the element in the jth row and ith column (a_ji).
Step 4: Write the condition in simple terms: If you switch the row and column of any element, you should get the opposite sign. For example, if a_12 = 3, then a_21 must be -3.
Step 5: Remember that the diagonal elements (where i equals j) must be zero because a_ii = -a_ii implies a_ii = 0.
Skew-Symmetric Matrix – A skew-symmetric matrix is one where the transpose of the matrix is equal to its negative, meaning that the elements satisfy the condition a_ij = -a_ji for all indices i and j.
