Matrix Algebra and Properties Quiz

To classify the type of matrix based on its dimensions

To determine the number of non-zero rows in its echelon form (correct)

To compute the inverse of the matrix

To find the eigenvalues of the matrix

Eigenvectors must always form a complete basis for the vector space. (correct)

An eigenvector associated with an eigenvalue can be scaled by any non-zero scalar.

Eigenvectors can be zero vectors only if the eigenvalue is zero.

Eigenvectors corresponding to distinct eigenvalues are linearly independent.

The adjoint represents only the diagonal elements of the inverse.

The inverse is equal to the adjoint divided by the determinant. (correct)

The adjoint can be calculated directly from the inverse.

Both the adjoint and inverse yield the same matrix if the original is singular.

<p>Four: Positive, Negative, Complex, Zero</p> Signup and view all the answers

<p>Canonical Form</p> Signup and view all the answers