In this question you are asked to findthe coordinate vector of -2 x 3 -2 x 2 +2

Question

In this question you are asked to findthe coordinate vector of -2 x3-2 x2+2 x-4 with respect to the basis
B = {x3+1,x2-x,2 x+1,1 } of P3.


3.1(1 mark) Firstly, what does it mean to find such avector? i.e. if [a, b, c, d] isthe required coordinate vector give an expression for -2 x3-2 x2+2 x-4.

Note. Your answer should be an appropriate linearcombination of polynomials. Only round brackets may be needed.There should be no square brackets.
-2 x3-2 x2+2 x-4 =


3.2(1 mark) Your last answer gives four equations inthe unknowns a, b, c, d, byreading off the corresponding coefficients of each power of x onboth sides of your answer to the last question part.

Give the equations in a, b, c,d you obtain by considering each power of x.

Note. Ensure the sides of your equationscorrespond to the sides of your equation in the last part.
3.2.1 (.25 marks)
coefficient of x3:


3.2.2 (.25 marks)
coefficient of x2:


3.2.3 (.25 marks)
coefficient of x:


3.2.4 (.25 marks)
constant coefficient:


3.3(1 mark) Now solve the equations you just foundand thus obtain the coordinate vector of -2 x3-2 x2+2 x-4 relative to basis B.

Enter your answer as a row vector using the list syntax, i.e. inthe form: [a, b, c, d]
Answer:
In this question you are asked to findthe coordinate vector of -2 x3-2 x2+2 x-4 with respect to the basis
B = {x3+1,x2-x,2 x+1,1 } of P3.


3.1(1 mark) Firstly, what does it mean to find such avector? i.e. if [a, b, c, d] isthe required coordinate vector give an expression for -2 x3-2 x2+2 x-4.

Note. Your answer should be an appropriate linearcombination of polynomials. Only round brackets may be needed.There should be no square brackets.
-2 x3-2 x2+2 x-4 =


3.2(1 mark) Your last answer gives four equations inthe unknowns a, b, c, d, byreading off the corresponding coefficients of each power of x onboth sides of your answer to the last question part.

Give the equations in a, b, c,d you obtain by considering each power of x.

Note. Ensure the sides of your equationscorrespond to the sides of your equation in the last part.
3.2.1 (.25 marks)
coefficient of x3:


3.2.2 (.25 marks)
coefficient of x2:


3.2.3 (.25 marks)
coefficient of x:


3.2.4 (.25 marks)
constant coefficient:


3.3(1 mark) Now solve the equations you just foundand thus obtain the coordinate vector of -2 x3-2 x2+2 x-4 relative to basis B.

Enter your answer as a row vector using the list syntax, i.e. inthe form: [a, b, c, d]
Answer:
3.1(1 mark) Firstly, what does it mean to find such avector? i.e. if [a, b, c, d] isthe required coordinate vector give an expression for -2 x3-2 x2+2 x-4.

Note. Your answer should be an appropriate linearcombination of polynomials. Only round brackets may be needed.There should be no square brackets.
-2 x3-2 x2+2 x-4 =

3.1(1 mark) Firstly, what does it mean to find such avector? i.e. if [a, b, c, d] isthe required coordinate vector give an expression for -2 x3-2 x2+2 x-4.

Note. Your answer should be an appropriate linearcombination of polynomials. Only round brackets may be needed.There should be no square brackets.
-2 x3-2 x2+2 x-4 =
3.2(1 mark) Your last answer gives four equations inthe unknowns a, b, c, d, byreading off the corresponding coefficients of each power of x onboth sides of your answer to the last question part.

Give the equations in a, b, c,d you obtain by considering each power of x.

Note. Ensure the sides of your equationscorrespond to the sides of your equation in the last part.
3.2.1 (.25 marks)
coefficient of x3:


3.2.2 (.25 marks)
coefficient of x2:


3.2.3 (.25 marks)
coefficient of x:


3.2.4 (.25 marks)
constant coefficient:

3.2(1 mark) Your last answer gives four equations inthe unknowns a, b, c, d, byreading off the corresponding coefficients of each power of x onboth sides of your answer to the last question part.

Give the equations in a, b, c,d you obtain by considering each power of x.

Note. Ensure the sides of your equationscorrespond to the sides of your equation in the last part.
3.2.1 (.25 marks)
coefficient of x3:


3.2.2 (.25 marks)
coefficient of x2:


3.2.3 (.25 marks)
coefficient of x:


3.2.4 (.25 marks)
constant coefficient:

3.2.1 (.25 marks)
coefficient of x3:

3.2.1 (.25 marks)
coefficient of x3:
3.2.2 (.25 marks)
coefficient of x2:

3.2.2 (.25 marks)
coefficient of x2:
3.2.3 (.25 marks)
coefficient of x:

3.2.3 (.25 marks)
coefficient of x:
3.2.4 (.25 marks)
constant coefficient:

3.2.4 (.25 marks)
constant coefficient:
3.3(1 mark) Now solve the equations you just foundand thus obtain the coordinate vector of -2 x3-2 x2+2 x-4 relative to basis B.

Enter your answer as a row vector using the list syntax, i.e. inthe form: [a, b, c, d]
Answer:
3.3(1 mark) Now solve the equations you just foundand thus obtain the coordinate vector of -2 x3-2 x2+2 x-4 relative to basis B.

Enter your answer as a row vector using the list syntax, i.e. inthe form: [a, b, c, d]
Answer:
In this question you are asked to findthe coordinate vector of -2 x3-2 x2+2 x-4 with respect to the basis
B = {x3+1,x2-x,2 x+1,1 } of P3.


3.1(1 mark) Firstly, what does it mean to find such avector? i.e. if [a, b, c, d] isthe required coordinate vector give an expression for -2 x3-2 x2+2 x-4.

Note. Your answer should be an appropriate linearcombination of polynomials. Only round brackets may be needed.There should be no square brackets.
-2 x3-2 x2+2 x-4 =


3.2(1 mark) Your last answer gives four equations inthe unknowns a, b, c, d, byreading off the corresponding coefficients of each power of x onboth sides of your answer to the last question part.

Give the equations in a, b, c,d you obtain by considering each power of x.

Note. Ensure the sides of your equationscorrespond to the sides of your equation in the last part.
3.2.1 (.25 marks)
coefficient of x3:


3.2.2 (.25 marks)
coefficient of x2:


3.2.3 (.25 marks)
coefficient of x:


3.2.4 (.25 marks)
constant coefficient:


3.3(1 mark) Now solve the equations you just foundand thus obtain the coordinate vector of -2 x3-2 x2+2 x-4 relative to basis B.

Enter your answer as a row vector using the list syntax, i.e. inthe form: [a, b, c, d]
Answer:

Explanation / Answer

never post too many questions in the same post. it is a kindof abuse. suppose -2 x3-2 x2+2 x-4 = a( x3+1) + b (x2-x)+c(2 x+1)+d(1) ==> a x3 + bx2 + ( 2c -b)x+ ( a-b +c+d) = -2 x3-2 x2+2 x-4 ==> a = -2 , b = -2 , 2c - b = 2 ==> 2c = 0 ==> c = 0, a - b + c + d = -4 ==> d = -4+ 2 -2 +0 ==> d =-4. the coordinate vector of the given vectorrelative to the given basis is ( -2,-2,0,-4).

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