The following polynomials are the first five in the sequence known as Chebyshev polynomials of the first kindT0(x)=1, T1(x)=x, T
2(x)=2x2 −1 T3(x)=4x3 −3x, T4(x)=8x4 −8x2 +1.(a) Show that {T0, T1, T2, T3, T4} is a basis for P4, the space of polynomials of degree ≤ 4.(b) Check that differentiation defines a linear transformation TD : P4 → P3 and write down the matrix of each linear transformation in the Chebyshev basis. Similarly, check that integration is a linear transformation TS : P3 → P4.(c) Let D and S be the differentiation and integration matrices, respectively, from part (b). Compute the matrix products DS and SD. Interpret the results using calculus: choose a suitable polynomial in P4, differentiate it, and then integrate it.(d) Write down bases for the null spaces and column spaces of D and S. Provide the cor- responding polynomials. Can you interpret your results about D and S in light of what you know about differentiation and integration from calculus?
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Answer:
<h2>not exist</h2>Step-by-step explanation:
The coordinates of the intersection of the line are the solution of the system of equations.
The system of equations has no solution. Therefore, the lines are parallel (the intersection does not exist).
Answer: 3
Step-by-step explanation:
Let say x the width of the tank,
x+4 its length,
x+2 its height
<u>width=3</u>
length=3+4=7
height=3+2=5