Question

1. A polynomial can be represented in Matlab as a vector of its coefficients, for example the polynomial p(x) = p_0 + p_1x + p_2x^2 + "..." + p_nx^n may be stored as p = [ p_0, p_1, p_2, ..., p_n]; Remember that MATLAB arrays always start their index at 1 and so the coeffi- cient of x^k in p(x) is stored in p(k-1). Do not use any inbuilt polynomial functions to answer this question. (a) Write a function MPR_Asgn4_Q1a_StudentID.m which takes as its argu- ments a vector containing the coefficients of a polynomial, and a scalar value of x or vector of such values, and returns a scalar (or vector) of value(s) of the polynomial evaluated at x. [2 marks] (b) Write a function named MPR_Asgn4_Q1b_StudentID.m which takes as its arguments two vectors representing polynomials a and b together with a string argument op. Your function should return the following result in a single output vector representing a polynomial c if op = '+' c is the sum of the two input polynomials; if op = '-' c is the difference of the two input polynomials; if op = '*' c is the product of the two input polynomials. As a reminder, to multiply two polynomials together you need to multi- ply each coefficient of the first polynomial with each coefficient of the second polynomial and add this to the appropriate coefficient of the resulting polynomial, for example a_1 x b_2 contributes to the coefficient of x^{1+2} = x^3 in the resulting polynomial, as does a_0 x b_3, a_2 x b_1 and a_3 x b_0. When coding this remember that vectors in MATLAB start indexing at 1.

          1. A polynomial can be represented in Matlab as a vector of its coefficients, for
example the polynomial
p(x) = p_0 + p_1x + p_2x^2 + "..." + p_nx^n
may be stored as
p = [ p_0, p_1, p_2, ..., p_n];
Remember that MATLAB arrays always start their index at 1 and so the coeffi-
cient of x^k in p(x) is stored in p(k-1).
Do not use any inbuilt polynomial functions to answer this question.
(a) Write a function MPR_Asgn4_Q1a_StudentID.m which takes as its argu-
ments a vector containing the coefficients of a polynomial, and a scalar
value of x or vector of such values, and returns a scalar (or vector) of
value(s) of the polynomial evaluated at x.
[2 marks]
(b) Write a function named MPR_Asgn4_Q1b_StudentID.m which takes as its
arguments two vectors representing polynomials a and b together with a
string argument op. Your function should return the following result in a
single output vector representing a polynomial c
if op = '+' c is the sum of the two input polynomials;
if op = '-' c is the difference of the two input polynomials;
if op = '*' c is the product of the two input polynomials.
As a reminder, to multiply two polynomials together you need to multi-
ply each coefficient of the first polynomial with each coefficient of the
second polynomial and add this to the appropriate coefficient of the
resulting polynomial, for example a_1 x b_2 contributes to the coefficient
of x^{1+2} = x^3 in the resulting polynomial, as does a_0 x b_3, a_2 x b_1 and
a_3 x b_0.
When coding this remember that vectors in MATLAB start indexing
at 1.

1. A polynomial can be represented in Matlab as a vector of its coefficients, for
example the polynomial
p(x) = p0 + p1x + p2x^2 + "..." + pnx^n
may be stored as
p = [ p0, p1, p2, ..., pn];
Remember that MATLAB arrays always start their index at 1 and so the coeffi-
cient of x^k in p(x) is stored in p(k-1).
Do not use any inbuilt polynomial functions to answer this question.
(a) Write a function MPRAsgn4Q1aStudentID.m which takes as its argu-
ments a vector containing the coefficients of a polynomial, and a scalar
value of x or vector of such values, and returns a scalar (or vector) of
value(s) of the polynomial evaluated at x.
[2 marks]
(b) Write a function named MPRAsgn4Q1bStudentID.m which takes as its
arguments two vectors representing polynomials a and b together with a
string argument op. Your function should return the following result in a
single output vector representing a polynomial c
if op = '+' c is the sum of the two input polynomials;
if op = '-' c is the difference of the two input polynomials;
if op = '*' c is the product of the two input polynomials.
As a reminder, to multiply two polynomials together you need to multi-
ply each coefficient of the first polynomial with each coefficient of the
second polynomial and add this to the appropriate coefficient of the
resulting polynomial, for example a1 x b2 contributes to the coefficient
of x^1+2 = x^3 in the resulting polynomial, as does a0 x b3, a2 x b1 and
a3 x b0.
When coding this remember that vectors in MATLAB start indexing
at 1.

Added by Nancy R.

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