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The solution of the system of equations
x+2y=4
2x+y=-2
is attempted by the Gauss
Jacobi and Gauss Seidel iteration schemes. Set up the two schemes in matrix form. Will the
iteration schemes converge? Justify your answer.
x+2y=4
2x+y=-2
is attempted by the Gauss
Jacobi and Gauss Seidel iteration schemes. Set up the two schemes in matrix form. Will the
iteration schemes converge? Justify your answer.
Solve the system of equations
8x-y+2z=4
-3x+11y-z+3t=23
-y+10z-t=-13
-2x+y-z+8t=13
with x^(0) = [0 0 0 0]^T , by using the Gauss Jacboi and Gauss Seidel method. The exact
solution of the system is x = [1 2 −1 1]^T . Perform the required number of iterations so that
the same accuracy is obtained by both the methods. What conclusions can you draw from the
results obtained?
8x-y+2z=4
-3x+11y-z+3t=23
-y+10z-t=-13
-2x+y-z+8t=13
with x^(0) = [0 0 0 0]^T , by using the Gauss Jacboi and Gauss Seidel method. The exact
solution of the system is x = [1 2 −1 1]^T . Perform the required number of iterations so that
the same accuracy is obtained by both the methods. What conclusions can you draw from the
results obtained?
Solve the following linear system Ax = b of equations with partial pivoting
x-y+3z=3
2x+y+4z=7
3x+5y-2z=6
Store the multipliers and also write the pivoting vectors.
x-y+3z=3
2x+y+4z=7
3x+5y-2z=6
Store the multipliers and also write the pivoting vectors.
Solve the system of equations
2x+3y+4z+t=3
x+2y+t=2
2x+3y+z-t=1
x-2y-z+4t=5
using Gauss elimination method with pivoting.
2x+3y+4z+t=3
x+2y+t=2
2x+3y+z-t=1
x-2y-z+4t=5
using Gauss elimination method with pivoting.
Observe a one-day cricket match to be held in the year 2016. Prepare a project report indicating the performance and comparision with respect to the following ponits: (i) Range of the individual scores of the players. (ii) Compute team wise mean deviation score. (iii) Prepare teamwise grouped frequency distribution tables, showing the number of overs as class intervals and corresponding scores as frequencies. (iv) Represent the above requency distribution table (Part iii) with the help of histogrames.
A person standing at the crossing at two straight paths represented by the equations 2x-3y-4 = 0 and 3x-4y-5 = 0, wants to reach a path represented by 6x-7y+8 = 0 in least time. Find the equations of path he should follow.
true/false?justify.
If lim n→∞ (u)subscript n =0, then the series (∞)∑(n=1) (u)subscipt n is convergent.
If lim n→∞ (u)subscript n =0, then the series (∞)∑(n=1) (u)subscipt n is convergent.
true/false? justify.
The function f defined by f(x) =|x −(5/2)| ,x∈R has a local maxima of x=5/2
The function f defined by f(x) =|x −(5/2)| ,x∈R has a local maxima of x=5/2
Show that the function f defined on R by
f(x)={3x^(2) cos(1)/(2x), when x≠0 ; 0, when x=0
is derivable on R but f ′ is not continuous at x=0
f(x)={3x^(2) cos(1)/(2x), when x≠0 ; 0, when x=0
is derivable on R but f ′ is not continuous at x=0
Find the upper and lower integrals of the function f defined by
f(x)= (7/2)-2x, ∀ x∈[1,3]
Is f integrable over the interval [1,3]? Justify.
f(x)= (7/2)-2x, ∀ x∈[1,3]
Is f integrable over the interval [1,3]? Justify.
