MATLAB Matrix and Vector Operations 2

Question 1

What does the MATLAB expression `A \ b` compute when A is a square matrix?

Accepted Answer

The solution x to the linear system A*x = b

Answer

The backslash operator solves the linear system A*x = b using efficient factorization, equivalent to inv(A)*b but numerically more stable.

Question 2

Which MATLAB function returns both eigenvalues and eigenvectors of a matrix A?

Accepted Answer

[V, D] = eig(A)

Answer

With two output arguments, eig returns V (eigenvectors as columns) and D (diagonal matrix of eigenvalues).

Question 3

What is the result of `dot([1 2 3], [4 5 6])` in MATLAB?

Accepted Answer

32

Answer

The dot product is 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Question 4

How do you extract the diagonal elements of matrix A as a column vector in MATLAB?

Accepted Answer

diag(A)

Answer

diag(A) extracts the main diagonal of matrix A and returns it as a column vector.

Question 5

What does `rank(A)` return for a 4x4 identity matrix?

Accepted Answer

4

Answer

The identity matrix has 4 linearly independent rows and columns, so its rank is 4 (full rank).

MATLAB - MATLAB Technical Computing Practice Test