Algebra Matlab Question

required answer only question 3

2. (a) Use Matlab/Octave to create a 6 x 6 matrix A such that A (the row i, column j
entry of A) is given by
Aij = j – i.
(Hint: one way is to use for loops.)
(b) Use Matlab/Octave to find the rank and nullity of your matrix, its reduced row
echelon form, and a basis for its row space, column space, and null space.
(Hint: Parts of matrices can be extracted using commands like A([1,3], :), which
returns a matrix containing rows 1 and 3 of matrix A.)
1
3. In this question you will use Matlab/Octave to find a degree-4 polynomial
y = p(x) = ax + b³
+ cx² + dx + e
that intersects the following (x, y) pairs:
4770-2
DEBLZE
I
-2 47
-1
1
1
2
11
(a) Set up a system of five equations involving a, b, c, d, and e Hint: For example,
substituting (x, y) = (1,2) into the polynomial p(x) gives the equation a+b+c+
d+e=2.
(b) Use Matlab/Octave to solve the system in (a).
(c) Use Matlab/Octave to plot the data and the polynomial on -2 ≤ x ≤ 2. Label
the axes and give the graph a title consisting of your name and ID number, e.g.
McLachlan 3141592.