Engineering Mathematics Mastery Hub: The Industry Foundation

Consider a square matrix $A$ of size $n \times n$. If the determinant of $A$ is non-zero, what can be definitively concluded about the linear system $Ax = b$ for any vector $b \in \mathbb{R}^n$?

In the context of matrix diagonalization, if a matrix $A$ has $n$ distinct eigenvalues, what can be stated about its eigenvectors?

focuses on the eigenvectors themselves. Option D is incorrect; eigenvalues can be zero, negative, or complex, and their distinctness is the key property here, not their sign. Question: For a symmetric matrix $A$, which of the following properties is always true regarding its eigenvalues and eigenvectors?