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Math
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.
Math
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?
Math
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.
Math
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.
If 50 (fifty) classes of 20 (twenty) students are randomly selected, what is the probability that 10 (ten) classes have no left-handed students if 8% of students in the class are left-handed students.
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.
Use truth table to test the validity of:
If I study, then I will not fail mathematics
if I don't play basketball, then I will study
But I failed mathematics
Therefore I must have played basketball
If I study, then I will not fail mathematics
if I don't play basketball, then I will study
But I failed mathematics
Therefore I must have played basketball
Suppose
y
=
2
e
−
4
x
y=2e−4x
is the solution to the initial value problem
y
′
+
k
y
=
0
,
y
(
0
)
=
y
0
y′+ky=0,y(0)=y0
. Find the value of
y
0
y
=
2
e
−
4
x
y=2e−4x
is the solution to the initial value problem
y
′
+
k
y
=
0
,
y
(
0
)
=
y
0
y′+ky=0,y(0)=y0
. Find the value of
y
0
Superior Construction Pte Ltd is a successful company dealing with many major projects in Singapore. Recently, it has submitted its biddings for two major Government projects. Project A worth about $120 million and the company believes it has 40% chance of securing the project. Project B worth $1.8 billion and has 30% chance the company will secure the project. Both projects are independent of each other. What is the probability that the company will secure Project A or B but not both?
Math
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.
