MATLAB Applications in Mathematics and Engineering

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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?

Through a trial version, student version, or licensed product Signup and view all the answers

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

Dealing with matrices and arrays Signup and view all the answers

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

All of the above Signup and view all the answers

What is a matrix in MATLAB?

A two-dimensional array of numbers Signup and view all the answers

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

With a semicolon Signup and view all the answers

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

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

What is the purpose of the Gaussian Elimination method?

To solve a system of linear equations Signup and view all the answers

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

To create a matrix of zeros Signup and view all the answers

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

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

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

x = [1.2927; 0.0244] Signup and view all the answers

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

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

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

To find the least squares solution of the system Ax = b 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]`?

The projection of the 100 vectors onto the vector v Signup and view all the answers

What is the vector `u` in the code?

u = [1; 7] Signup and view all the answers

What is the result of the code `P*u`?

[-2; 1] Signup and view all the answers

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

Three Signup and view all the answers

What is the formula to find ui in Case 2?

ui = Avi / σi Signup and view all the answers

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

A is symmetric and positive definite Signup and view all the answers

What is the size of matrix V in Case 1?

3x3 Signup and view all the answers

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

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

What is the size of matrix U in Case 2?

3x3 Signup and view all the answers

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

To factorize a matrix into an orthogonal matrix and an upper triangular matrix Signup and view all the answers

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

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

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

Q is an orthogonal matrix and R is an upper triangular matrix Signup and view all the answers

What is the purpose of the isAlways function in MATLAB?

To check if a matrix equation is always true Signup and view all the answers

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

It is more stable than other methods 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?

The solution to the matrix equation Ax=b Signup and view all the answers