190k views
1 vote
Suppose the following information is known about matrix A.

a) A is a square matrix
b) A is a symmetric matrix
c) A is a singular matrix
d) A is a diagonal matrix

1 Answer

2 votes

Final answer:

The question analyzes the properties of matrix A, which is square, symmetric, singular, and diagonal. These terms indicate that A has equal rows and columns, is identical to its transpose, has no inverse, and has all non-diagonal elements as zero. Since it is singular, all diagonal elements must be zero, making A a zero matrix.

Step-by-step explanation:

The question pertains to the properties of a matrix A. Given that matrix A is a square matrix, symmetric, singular, and diagonal, we should understand what each of these terms means:

  • Square matrix: A matrix is square if it has the same number of rows and columns.
  • Symmetric matrix: A matrix is symmetric if the element at the ith row and jth column is the same as the element at the jth row and ith column, meaning A = AT.
  • Singular matrix: A matrix is singular (or noninvertible) if it does not have an inverse, which typically means its determinant is zero.
  • Diagonal matrix: A diagonal matrix is a matrix where all off-diagonal entries are zero. Only the diagonal elements (top left to bottom right) may be non-zero.

Since matrix A is also singular, all diagonal elements in this case must be zero because a nonzero determinant would imply that the matrix is invertible. Hence, A is a zero matrix.

User Gigimon
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories