[SOLVED] AMITH 350 - Assignment 01

Solve all the following problems in MATLAB.

1. Enter the following matrix A and create

• A 4 × 5 matrix B from the 1^st , 3^rd and 5^th rows and 1^st , 2^nd , 4^th and 8^th columns of the matrix A.
• 16-elements row vector C from the elements of the 5^th row and the 4^th and 6^th columns of the matrix A.

2. Define 𝑎 𝑎𝑛𝑑 𝑏 as scalar 𝑎 = 0.75 and 𝑏 = 11.3 and 𝑥, 𝑦, 𝑧 as the vectors

𝑥 = [2,5,1,9, ], 𝑦 = [0.2, 1.1, 1.8, 2] and 𝑧 = [−3, 2, 5, 4], then evaluate

3. Solve the following system of equations

2𝑥₁ + 𝑥₂ + 𝑥₃ − 𝑥₄ = 12

𝑥₁ + 5𝑥₂ − 5𝑥₃ + 6𝑥₄ = 35

−7𝑥₁ + 3𝑥₂ − 7𝑥₃ − 5𝑥₄ = 7

𝑥₁ − 5𝑥₂ + 2𝑥₃ + 7𝑥₄ = 21

4. Plot sin² 𝑥, cos² 𝑥 𝑎𝑛𝑑 cos 2𝑥 on the same plot as well as subplots for 0 ≤ 𝑥 ≤ 2𝜋, in different styles.
5. Consider the function 𝑧 = 0.56 cos(𝑥𝑦). Draw a surface plot showing variation of 𝑧 with 𝑥 and 𝑦. Given 𝑥 ∈ [0,10]𝑎𝑛𝑑 𝑦 ∈ [0,100]
6. Write a function to find the gradient of 𝑓(𝑥, 𝑦) = 𝑥² + 𝑦² − 2𝑥𝑦 + 4 at (a) (1,1) and (b) (1, −2). Use the function name from command prompt as well as from a script file.
7. Use symbolic toolbox to solve the following problems (a) Solve 𝑥⁷ − 8𝑥⁵ + 7𝑥⁴ + 5𝑥³ − 8𝑥 + 9 = 0

(b) Solve the ODE:

, then evaluate 𝐹′(𝑥) and 𝐹′′(𝑥).

8. The population of X from the year 1930 to the year 2020 is given in the following table:

• Fit the data with a second-order polynomial. Make a plot of the points and the polynomial.
• Fit the data with linear and spline interpolations. Estimate the population in 1995 with linear and spline interpolations.