Help!! How to solve these matlab problems?

Question

Problem1:

Enter the following data into the Matlab command window.

A=[02: 1 4];

B=[1 3; 2 6]:

What is A*B? What is A.*B?

What does A.^-I produce verses A^-1?

Problem3:

Given the matrix: M=[1 1; 1 3;]; Use loops to determine how many

of the entries are greater than I and the location of all qualifying entries (the corresponding row and column)

Problem4:

Find Taylor series using MATLAB for the following functions:

1. sin(x) up to 6^th order

2. cos(x) up to 8^th order

3. 1/1-x up to 10^th order

Problem5:

Using the Newton-Raphson routine determine the zero of the function

• f(x)= e^x - e^-2x+ 1.

Answer 1

Problem 5:

the approximate solutions is -0.281199574322961846512 after 7 iterations, and is correct to 21 digits

Problem 4:

1) x -x^3/6 + x^5/120 - x^7/5040 + O(x^8)

2)

1 - x^2/2 + x^4/24 - x^6/720 + x^8/40320 + O(x^10)

3) 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+O(x^11)

A*B = [0 2] [1 3]

[1 4] [2 6]

= [ 4 12]

[ 9 27]

0 2 | 1 0

1 4 | 0 1

-2*row1+row2

0 2 | 1 0

1 0 | -2 1

1/2 row1

0 1 | 1/2 0

1 0 | -2 1

inverse is [ -2 1 ]

[ 1/2 0 ]

multiplies original by inverse

[ 0 2 | -2 1 ]

[ 1 4 | 1/2 0 ]

the product is the identity