Linear Algebra Concepts Quiz

The rank becomes zero

The rank remains unchanged (correct)

The rank increases by 1

The rank decreases by 1

Eigenvalues and eigenvectors (correct)

System of linear equations

Symmetric matrices

Orthogonal matrices

Skew symmetric matrix (correct)

Orthogonal matrix

Symmetric matrix

Diagonal matrix

<p>Eigenvalues and eigenvectors of a matrix are values and vectors that satisfy the equation Av = λv, where A is a square matrix, v is a non-zero vector, and λ is a scalar. The eigenvectors are the non-zero vectors that satisfy this equation, and the eigenvalues are the corresponding scalars.</p> Signup and view all the answers

<p>The Cayley-Hamilton Theorem states that every square matrix satisfies its own characteristic equation. In other words, if A is a square matrix, then the characteristic polynomial of A, denoted by p(λ), when evaluated at A, results in the zero matrix: p(A) = 0.</p> Signup and view all the answers

<p>Symmetric matrices are square matrices that are equal to their transpose: A = A^T. Skew-symmetric matrices are square matrices that satisfy the property A^T = -A. Orthogonal matrices are square matrices that satisfy the property A^T * A = A * A^T = I, where I is the identity matrix.</p> Signup and view all the answers