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About 3307 results. 1294 free access solutions
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free/or 0.5$ |
| m53935 | Find the eigenvalues and associated eigenvectors of the following 3 × 3 matrices. Is there a set of linearly independent eigenvectors?
a.
b.
c.
d. |
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| m53953 | Find the first three iterations obtained by the Power method applied to the following matrices.
a.
Use x(0) = (1,−1, 2)t.
b.
Use x(0) = (−1, 0, 1)t.
c.
Use x(0) = (−1, 2, 1)t.
d.
Use x(0) = (1,−2, 0, 3)t. |
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| m53954 | Find the first three iterations obtained by the Power method applied to the following matrices.
a.
Use x(0) = (1, 2, 1)t.
b.
Use x(0) = (1, 1, 0, 1)t.
c.
Use x(0) = (1, 1, 0,−3)t.
d.
Use x(0) = (0, 0, 0, 1)t. |
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| m53955 | Find the first three iterations obtained by the Symmetric Power method applied to the following matrices.
a.
Use x(0) = (1,−1, 2)t.
b.
Use x(0) = (−1, 0, 1)t.
c.
Use x(0) = (0, 1, 0)t.
d.
Use x(0) = (0, 1, 0, 0)t. |
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| m53956 | Find the first three iterations obtained by the Symmetric Power method applied to the following matrices.
a.
Use x(0) = (1,−1, 2)t.
b.
Use x(0) = (−1, 0, 1)t.
c.
Use x(0) = (1, 0, 0, 0)t.
d.
Use x(0) = (1, 1, 0,−3)t. |
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| m53957 | Find the first two iterations of the Jacobi method for the following linear systems, using x(0) = 0:
a. 3x1 − x2 + x3 = 1,
3x1 + 6x2 + 2x3 = 0,
3x1 + 3x2 + 7x3 = 4.
b. 10x1 − x2 = 9,
−x1 + 10x2 − 2x3 = 7,
− 2x2 + 10x3 = 6.
c. 10x1 + 5x2 = 6,
5x1 + 10x2 − 4x3 = 25,
− 4x2 + 8x3 − x4 = −11,
− x3 + 5x4 = −11.
d. 4x1 + x2 + x3 + x5 = 6,
−x1 − 3x2 + x3 + x4 = 6,
2x1 + x2 + 5x3 − x4 − x5 = 6,
−x1 − x2 − x3 + 4x4 = 6,
2x2 − x3 + x4 + 4x5 = 6 |
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| m53958 | Find the first two iterations of the Jacobi method for the following linear systems, using x(0) = 0:
a. 4x1 + x2 − x3 = 5,
−x1 + 3x2 + x3 = −4,
2x1 + 2x2 + 5x3 = 1.
b. −2x1+ x2 + 1/2 x3 = 4,
x1−2x2 - 1/2 x3 = −4,
x2 + 2x3 = 0.
c. 4x1 + x2 − x3 + x4 = −2,
x1 + 4x2 − x3 − x4 = −1,
−x1 − x2 + 5x3 + x4 = 0,
x1 − x2 + x3 + 3x4 = 1.
d. 4x1 − x2 − x4 = 0,
−x1 + 4x2 − x3 − x5 = 5,
− x2 + 4x3 − x6 = 0,
−x1 + 4x4 − x5 = 6,
− x2 − x4 + 4x5 − x6 = −2,
− x3 − x5 + 4x6 = 6. |
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| m53959 | Find the first two iterations of the SOR method with ω = 1.1 for the following linear systems, using x(0) = 0:
a. 3x1 − x2 + x3 = 1,
3x1 + 6x2 + 2x3 = 0,
3x1 + 3x2 + 7x3 = 4.
b. 10x1 − x2 = 9,
−x1 + 10x2 − 2x3 = 7,
− 2x2 + 10x3 = 6.
c. 10x1 + 5x2 = 6,
5x1 + 10x2 − 4x3 = 25,
− 4x2 + 8x3 − x4 = −11,
− x3 + 5x4 = −11.
d. 4x1 + x2 + x3 + x5 = 6,
−x1 − 3x2 + x3 + x4 = 6,
2x1 + x2 + 5x3 − x4 − x5 = 6,
−x1 − x2 − x3 + 4x4 = 6,
2x2 − x3 + x4 + 4x5 = 6 |
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| m53960 | Find the first two iterations of the SOR method with ω = 1.1 for the following linear systems, using x(0) = 0:
a. 4x1 + x2 − x3 = 5,
−x1 + 3x2 + x3 = −4,
2x1 + 2x2 + 5x3 = 1.
b. −2x1+ x2 + 1/2 x3 = 4,
x1−2x2 - 1/2 x3 = −4,
x2 + 2x3 = 0.
c. 4x1 + x2 − x3 + x4 = −2,
x1 + 4x2 − x3 − x4 = −1,
−x1 − x2 + 5x3 + x4 = 0,
x1 − x2 + x3 + 3x4 = 1.
d. 4x1 − x2 = 0,
−x1 + 4x2 − x3 = 5,
− x2 + 4x3 = 0,
+ 4x4 − x5 = 6,
− x4 + 4x5 − x6 = −2,
− x5 + 4x6 = 6. |
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| m53961 | Find the fourth Taylor polynomial P4(x) for the function f (x) = x(ex)2 about x0 = 0.
a. Find an upper bound for |f (x) − P4(x)|, for 0 ≤ x ≤ 0.4.
b. Approximate
c. Find an upper bound for the error in (b) using
d. Approximate f (0.2) using P 4(0.2), and find the error. |
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| m53963 | Find the general continuous least squares trigonometric polynomial Sn(x) for f (x)= ex on [−π, π]. |
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| m53964 | Find the general continuous least squares trigonometric polynomial Sn(x) for |
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| m53965 | Find the general continuous least squares trigonometric polynomial Sn(x) in for |
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| m53972 | Find the largest interval in which p∗ must lie to approximate p with relative error at most 10−4 for each value of p
a. π
b. e
c.√2
d. 3√7 |
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| m53973 | Find the least squares polynomial approximation of degree 2 on the interval [−1, 1] for the functions in Exercise 3.
In Exercise 3
a. f (x) = x2 + 3x + 2, [0, 1];
b. f (x) = x3, [0, 2];
c. f (x) = 1/x, [1, 3];
d. f (x) = ex , [0, 2];
e. f (x) = 1/2 cos x + 1/3 sin 2x, [0, 1];
f. f (x) = x ln x, [1, 3]. |
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| m53974 | Find the least squares polynomial approximation of degree two to the functions and intervals in Exercise 1.
In Exercise 1
a. f (x) = x2 + 3x + 2, [0, 1];
b. f (x) = x3, [0, 2];
c. f (x) = 1/x, [1, 3];
d. f (x) = ex , [0, 2];
e. f (x) = 1/2 cos x + 1/3 sin 2x, [0, 1];
f. f (x) = x ln x, [1, 3]. |
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| m53975 | Find the least squares polynomials of degrees 1, 2, and 3 for the data in the following table. Compute the error E in each case. Graph the data and the polynomials. |
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| m53976 | Find the least squares polynomials of degrees 1, 2, and 3 for the data in the following table. Compute the error E in each case. Graph the data and the polynomials. |
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| m53989 | Find the linear least squares polynomial approximation on the interval [−1, 1] for the following functions.
a. f (x) = x2 − 2x + 3
b. f (x) = x3
c. f (x) = 1/(x + 2)
d. f (x) = ex
e. f (x) = 1/2 cos x + 1/3 sin 2x
f. f (x) = ln(x + 2) |
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| m53990 | Find the linear least squares polynomial approximation to f (x) on the indicated interval if
a. f (x) = x2 + 3x + 2, [0, 1];
b. f (x) = x3, [0, 2];
c. f (x) = 1/x, [1, 3];
d. f (x) = ex , [0, 2];
e. f (x) = 1/2 cos x + 1/3 sin 2x, [0, 1];
f. f (x) = x ln x, [1, 3]. |
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