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MATLAB: Functions, Vectors, and Equations

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MATLAB: Functions, Vectors, and Equations

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Questions and Answers

Which of the following MATLAB commands correctly represent the integral of the function $f(x, y, z) = x^{2}e^{y} - 5z^{2}$ with respect to x?

integral2(@(x,y) x^2 * exp(y) - 5*z^2, 0, 1, 0, 1)

int(x^2 * exp(y) - 5*z^2, x) (correct)

integrate(x^2 * exp(y) - 5*z^2, x)

integral(@(x) x^2 * exp(y) - 5*z^2, 0, 1) (correct)

The MATLAB command for performing element-wise multiplication on two vectors is `.*`.

True

What method is used to solve the system of equations provided in Q.3?

Gauss elimination

In the context of Lagrange's interpolation formula, if the $x$ values are 2, 3, and 4, the corresponding $y$ values are ________.

<p>1.4142, 1.7321, 2.0</p> Signup and view all the answers

Match the MATLAB operations with their descriptions:

<p>A. Element-wise addition = 1. x + y B. Element-wise division = 2. x ./ y C. Integral computation = 3. integral(@(x) f(x), 0, 1) D. Gauss elimination method = 4. A method for solving linear equations</p> Signup and view all the answers

Study Notes

MATLAB Commands

Q1: Calculate the integral and second derivative of the function f(x, y, z) = x²e^y - 5z² with respect to x and z using MATLAB.

Vector Operations in MATLAB

Q2: Create two vectors of the same length in MATLAB. Perform operations like addition, subtraction, element-wise multiplication, and element-wise division on these vectors.

Solving Linear Equations with Gauss Elimination

Q3: Solve the system of linear equations using MATLAB and the Gauss elimination method (without pivoting)
2x₁ + 8x₂ + 2x₃ = 14
x₁ + 6x₂ - x₃ = 13
2x₁ - x₂ + 2x₃ = 5

Lagrange's Interpolation Formula

Q4: Use Lagrange's interpolation formula to evaluate y(2.5) from the provided table.
X values (x) are 2, 3, 4
Y values (y) are 1.4142, 1.7321, 2.0

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Description

Test your skills in MATLAB with this quiz covering integral calculations, vector operations, linear equations solving using Gauss elimination, and Lagrange's interpolation. Each question is designed to challenge your understanding and application of MATLAB commands and mathematical concepts.