MATLAB Variables and Assignments
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Questions and Answers

What is the result of multiplying the transpose of an orthogonal matrix by itself?

  • A zero matrix
  • A symmetric matrix
  • A diagonal matrix
  • An identity matrix (correct)

What is the type of matrix R in the QR decomposition A = QR?

  • Lower triangular matrix
  • Diagonal matrix
  • Upper triangular matrix (correct)
  • Orthogonal matrix

What is the condition for the uniqueness of the QR decomposition of a matrix A?

  • A is a nonsingular matrix (correct)
  • A is a singular matrix
  • A is a diagonal matrix
  • A is a square matrix

What is the purpose of the Gram-Schmidt process in the QR decomposition?

<p>To orthogonalize a set of vectors (D)</p> Signup and view all the answers

What is the matrix Q in the QR decomposition of a matrix A?

<p>An orthogonal matrix (D)</p> Signup and view all the answers

What is the MATLAB command to initiate a matrix of zeros with 3 rows and 3 columns?

<p>Q=zeros(3,3) (D)</p> Signup and view all the answers

What happens when an expression returns a result that is not assigned to any variable?

<p>The system assigns it to a variable named answer (B)</p> Signup and view all the answers

What is the purpose of the 'who' command in MATLAB?

<p>To display the names of all variables (B)</p> Signup and view all the answers

What is the default display format for numbers in MATLAB?

<p>Four decimal place values (D)</p> Signup and view all the answers

What happens when you use the 'clear' command without specifying any variable in MATLAB?

<p>It deletes all variables from the memory (B)</p> Signup and view all the answers

How can you extend a long assignment to another line in MATLAB?

<p>Using a new line with the continuation of the assignment (D)</p> Signup and view all the answers

What is the purpose of the 'whos' command in MATLAB?

<p>To display the names and sizes of all variables (B)</p> Signup and view all the answers

What is the purpose of the loop variable 'i' in the Matlab code for Gauss Elimination?

<p>To iterate through the columns of the matrix (A)</p> Signup and view all the answers

What is the output of the Gauss Elimination method for the given system of equations?

<p>x = -1 1 2 (B)</p> Signup and view all the answers

What is the purpose of the command 'A(j,:) = A(j,:) - m*A(i,:)' in the Gauss Elimination Matlab code?

<p>To perform the row operations (D)</p> Signup and view all the answers

What is the name of the process used in the Matlab code to orthogonalize the matrix?

<p>Gram-Schmidt orthogonalization (C)</p> Signup and view all the answers

What is the purpose of the command 'x(n) = A(n,n+1)/A(n,n)' in the Gauss Elimination Matlab code?

<p>To solve for the variable x(n) (A)</p> Signup and view all the answers

What is the purpose of the command 'summ = summ + A(i,j)*x(j,:)' in the Gauss Elimination Matlab code?

<p>To solve for the variable x(i) (A)</p> Signup and view all the answers

What is the purpose of the matrix P in the context of projection matrices and least squares?

<p>To project a vector onto another vector (D)</p> Signup and view all the answers

What is the result of the code P*u in the provided example?

<p>A 2x100 matrix where each column is a vector projected onto the vector v (D)</p> Signup and view all the answers

What is the interpretation of the relative residual in the output of the lsqr function?

<p>The ratio of the norm of the residual vector to the norm of the right-hand side vector (D)</p> Signup and view all the answers

What is the relationship between the vectors u and v in the provided example?

<p>u is projected onto v (A)</p> Signup and view all the answers

What is the purpose of the hold on command in the provided code?

<p>To hold the current plot and add new data to it (B)</p> Signup and view all the answers

What is the primary goal of finding the least square fit for a system of equations?

<p>To minimize the sum of the squares of the errors (B)</p> Signup and view all the answers

What is the name of the process used to find the point on a plane that is closest to a given point?

<p>Projection (D)</p> Signup and view all the answers

What is the purpose of computing the SVD of a matrix?

<p>To diagonalize the matrix (C)</p> Signup and view all the answers

What is the correct order of steps to compute the SVD of a matrix A?

<p>Find AAT, find eigenvalues, find eigenvectors, normalize them (C)</p> Signup and view all the answers

What is the relationship between the singular values and eigenvalues of a matrix A?

<p>σ1 = λ1 and σ2 = λ2 (A)</p> Signup and view all the answers

What is the purpose of normalizing the eigenvectors in the SVD process?

<p>To make the eigenvectors orthonormal (C)</p> Signup and view all the answers

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