Eigenvalues and eigenvectors (eig) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute eigenvalues of matrix A.

MATLAB

A = [2 1; 1 2];
lambda = [1](A);

Drag options to blanks, or click blank then click option'

Adet

Brank

Cinv

Deig

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'inv' instead of 'eig' to compute eigenvalues.

Using 'det' which returns determinant, not eigenvalues.

The eig function computes eigenvalues of a matrix.

2fill in blank

medium

Complete the code to compute eigenvectors of matrix B.

MATLAB

B = [4 0; 1 3];
[V, D] = [1](B);

Drag options to blanks, or click blank then click option'

Aeig

Binv

Csvd

Dchol

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'svd' which computes singular value decomposition, not eigenvectors.

Using 'chol' which computes Cholesky decomposition.

The eig function returns eigenvectors and eigenvalues when called with two outputs.

3fill in blank

hard

Fix the error in the code to correctly compute eigenvalues of matrix C.

MATLAB

C = [1 2; 3 4];
lambda = eig[1]C);

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A(

B[

C{

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using square brackets or curly braces instead of parentheses.

Missing the opening parenthesis causes syntax error.

The function call syntax requires parentheses around the argument: eig(C).

4fill in blank

hard

Fill both blanks to create a dictionary of eigenvalues and eigenvectors for matrix D.

MATLAB

D = [5 2; 2 5];
[V, [1]] = eig(D);
eigenvalues = diag([2]);

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AD

BV

DV'

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning eigenvectors to the second output instead of eigenvalues.

Using the wrong variable inside diag function.

The second output of eig is the diagonal matrix of eigenvalues, so D is assigned to {{BLANK_1}}. To get eigenvalues as a vector, use diag(D).

5fill in blank

hard

Fill all three blanks to compute eigenvalues and eigenvectors, then normalize eigenvectors of matrix E.

MATLAB

E = [3 1; 0 2];
[[1], [2]] = eig(E);
norm_vec = [3]( [1](:,1) );

Drag options to blanks, or click blank then click option'

AV

BD

Cnorm

Deig

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping eigenvectors and eigenvalues in assignment.

Using eig function instead of norm to normalize.

eig returns eigenvectors and eigenvalues. We assign eigenvectors to V and eigenvalues to D. To normalize the first eigenvector, use norm(V(:,1)).