Chapter 9 Multiple choice questions

* not completed

. Which algebraic operation is not permitted for matrices?

Addition. correct incorrect

Subtraction. correct incorrect

Multiplication. correct incorrect

Division by a matrix. correct incorrect

* not completed

. Which of the following is not true, in general, for square matrices?

A ± B = B ± A correct incorrect

A x B = B x A correct incorrect

det(A x B) = det(A) x det(B) correct incorrect

(A x B)^T = B^T x A^T correct incorrect

* not completed

. Which of the following is not consistent with the other three?

The matrix A has an inverse, A^-1. correct incorrect

The rows, and columns, of A are linearly independent. correct incorrect

det(A) = 0. correct incorrect

None of the eigenvalues of A are equal to zero. correct incorrect

* not completed

. Which of the following is not true, in general, for Hermitian matrices?

They are symmetric, A^T = A. correct incorrect

Their eigenvalues are real. correct incorrect

Their eigenvectors are, or can be chosen to be, orthogonal. correct incorrect

They can be diagonalised. correct incorrect

* not completed

. Which of the following is not true for simultaneous equations?

They can be written in matrix notation if they are linear. correct incorrect

The solution is always unique if there are as many equations as unknowns. correct incorrect

There may be no solutions if the associated matrix is singular. correct incorrect

Non-trivial solutions for the case when the right-hand-side is equal to zero only exist if the associated matrix is singular. correct incorrect