Find the inverse of the matrix using Gauss-Jordan method.
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Determine a unique polynomial f(x) of degree such that
,
,
,
, where
.
For the following data, use Gauss backward difference method to obtain the interpolating polynomial f(x):
| x | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 |
| f(x) | 1.40 | 1.56 | 1.76 | 2.00 | 2.28 |
निम्नलिखित समीकरण निकाय को हल करने के लिए गाउस–सीडल पुनरावृत्ति विधि को आव्यूह रूप में स्थापित कीजिए :
$
दिखाइए कि पुनरावृत्ति विधि अभिसरित होती है और अतः इसकी अभिसरण दर ज्ञात कीजिए। (5)
Is , for any two ideals I and J of a ring R? Give reasons for your answer.
Using Classical Runge-Kutta fourth order method, find an approximate value of y(1.2) for the IVP ,
with
.
For an ideal I of a commutative ring R, define. Show that
i) is an ideal of R.
ii) .
iii) in some cases.
Divide the polynomial
x5 - 6x4 + 8x3 + 8x2 + 4x - 40
by (x - 3) by the synthetic division method and find the remainder.