MATLAB Applications in Mathematics and Engineering
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Questions and Answers

What is one of the primary uses of MATLAB in various fields?

  • Creating 2D and 3D graphics
  • Developing control systems (correct)
  • Simulating physics experiments
  • Analyzing algebraic equations

    • What is the main area where commands can be entered in the MATLAB environment?

  • Project Folder panel
  • Current Folder panel
  • Command Window (correct)
  • Desktop panel

    • What is the purpose of the Current Folder panel in the MATLAB environment?

  • To access project folders and files (correct)
  • To view graphical outputs
  • To set up the local environment
  • To enter commands at the command line

    • How can you obtain a MATLAB environment for use?

    <p>Through a trial version, student version, or licensed product</p> Signup and view all the answers

    What is one of the mathematical calculations that MATLAB is used for?

    <p>Dealing with matrices and arrays</p> Signup and view all the answers

    What is one of the fields where MATLAB is widely used as a computational tool?

    <p>All of the above</p> Signup and view all the answers

    What is a matrix in MATLAB?

    <p>A two-dimensional array of numbers</p> Signup and view all the answers

    How do you terminate a row when creating a matrix in MATLAB?

    <p>With a semicolon</p> Signup and view all the answers

    What is the purpose of the 'size' function in MATLAB?

    <p>To get the number of equations/variables in a matrix</p> Signup and view all the answers

    What is the purpose of the Gaussian Elimination method?

    <p>To solve a system of linear equations</p> Signup and view all the answers

    What is the purpose of the 'zeros' function in MATLAB?

    <p>To create a matrix of zeros</p> Signup and view all the answers

    How do you create a 3-by-3 matrix in MATLAB?

    <p>A = [1 2 3; 4 5 6; 7 8 9]</p> Signup and view all the answers

    What is the output of the code x = lsqr(A, b)?

    <p>x = [1.2927; 0.0244]</p> Signup and view all the answers

    What is the projection matrix P that projects any vector onto v = [-4; 2]?

    <p>P = [0.8, -0.4; -0.4, 0.2]</p> Signup and view all the answers

    What is the purpose of the lsqr function in the code?

    <p>To find the least squares solution of the system Ax = b</p> Signup and view all the answers

    What does the plot show after projecting the 100 vectors in matrix U onto the vector v = [-4; 2]?

    <p>The projection of the 100 vectors onto the vector v</p> Signup and view all the answers

    What is the vector u in the code?

    <p>u = [1; 7]</p> Signup and view all the answers

    What is the result of the code P*u?

    <p>[-2; 1]</p> Signup and view all the answers

    What is the number of eigenvalues of ATA in Case 1?

    <p>Three</p> Signup and view all the answers

    What is the formula to find ui in Case 2?

    <p>ui = Avi / σi</p> Signup and view all the answers

    What is the condition for SVD to be same as diagonalization in Case 3?

    <p>A is symmetric and positive definite</p> Signup and view all the answers

    What is the size of matrix V in Case 1?

    <p>3x3</p> Signup and view all the answers

    How do you find v3 in Step 8 of Case 1?

    <p>Using orthogonality (v3 is orthogonal to v1 and v2)</p> Signup and view all the answers

    What is the size of matrix U in Case 2?

    <p>3x3</p> Signup and view all the answers

    What is the purpose of the QR Decomposition with Gram-Schmidt process?

    <p>To factorize a matrix into an orthogonal matrix and an upper triangular matrix</p> Signup and view all the answers

    What is the command used to find the QR factorization of a matrix in MATLAB?

    <p>[Q,R] = qr(A)</p> Signup and view all the answers

    What is the output of the command [Q,R] = qr(A) when A is a Pascal matrix?

    <p>Q is an orthogonal matrix and R is an upper triangular matrix</p> Signup and view all the answers

    What is the purpose of the isAlways function in MATLAB?

    <p>To check if a matrix equation is always true</p> Signup and view all the answers

    What is the advantage of using QR decomposition to solve a matrix equation of the form Ax=b?

    <p>It is more stable than other methods</p> Signup and view all the answers

    What is the result of the command X = R\C when [C,R] = qr(A,b) is used to solve the matrix equation Ax=b?

    <p>The solution to the matrix equation Ax=b</p> Signup and view all the answers

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