Using a Power Series In Exercises 19-28, use the power series 1 1 + x = ∑ n = 0 ∞ ( − 1 ) n x n , | x | < 1 to find a power series for the function, centered at 0, and determine the interval or convergence. f ( x ) = ln ( 1 − x 2 ) = ∫ 1 1 + x d x − ∫ 1 1 − x d x
Using a Power Series In Exercises 19-28, use the power series 1 1 + x = ∑ n = 0 ∞ ( − 1 ) n x n , | x | < 1 to find a power series for the function, centered at 0, and determine the interval or convergence. f ( x ) = ln ( 1 − x 2 ) = ∫ 1 1 + x d x − ∫ 1 1 − x d x
Solution Summary: The author explains the power series of the given function f(x), centered at 0 and determine the interval of convergence.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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