let us create a variable for a row vector a = [1, 4, 1, 3, 2,...
let us create a variable for a row vector a = [1, 4, 1, 3, 2, 5,
0] and calculate the mean value of its elements using the Matlab
function ‘mean’ and store this value in variable aMean. Fig. 1
gives the Matlab code to do this.
a = [1, 4, 1, 3, 2, 5, 0];
aMean = mean(a);
Figure 1: Matlab code – row vector and mean of its elements.
Let us now construct a row vector b that...
Determine whether the following sets define vector spaces over
R:
(a) A={x∈R:x=k^2,k∈R}
(b) B={x∈R:x=k^2,k∈Z}
(c) C...
Determine whether the following sets define vector spaces over
R:
(a) A={x∈R:x=k^2,k∈R}
(b) B={x∈R:x=k^2,k∈Z}
(c) C ={p∈P^2 :p=ax^2,a∈R}
(d) D={z∈C:|z|=1}
(e) E={z∈C:z=a+i,a∈R}
(f) F ={p∈P^2 : d (p)∈R}
Using R and install.packages("MASS"), library(MASS)
1. Generate the following vector using at least two methods.
0,...
Using R and install.packages("MASS"), library(MASS)
1. Generate the following vector using at least two methods.
0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4
2. Generate the following vector.
Apple1, Banana2, Orange3, Cranberry4,
Watermelon5
3. Generate the following vector using the “rep” function.
a, a, b, b, c, c, a, a, b, b, c, c
4. In vector y = (8, 3, 5, 7, 6, 6, 8, 9, 2, 3, 9, 4, 10, 4,
11), which elements of y contains...
6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3...
6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3 + 1 2 t
2 i (a) Find r 0 (t) (b) Find the unit tangent vector to the space
curve of r(t) at t = 3. (c) Find the vector equation of the tangent
line to the curve at t = 3
Consider the following subset:
W =(x, y, z) ∈ R^3; z = 2x - y from...
Consider the following subset:
W =(x, y, z) ∈ R^3; z = 2x - y from R^3.
Of the following statements, only one is true. Which?
(1) W is not a subspace of R^3
(2) W is a subspace of R^3
and {(1, 0, 2), (0, 1, −1)} is a base of W
(3) W is a subspace of R^3
and {(1, 0, 2), (1, 1, −3)} is a base of W
(4) W is a subspace of R^3
and...
(1) Use ‘sample’ function to generate a vector of 100 random
numbers that follows a multinomial...
(1) Use ‘sample’ function to generate a vector of 100 random
numbers that follows a multinomial distribution with probability
(0.1, 0.15, 0.3, 0.45).
(2) Without using the ‘sample’ function, generate a vector of
100 random numbers that follows a multinomial distribution with
probability (0.1, 0.15, 0.3, 0.45).
(3) Calculate the probability for 2.5 < X < 9 in a Poisson
distribution with the mean 6. (using R)
1. A plane curve has been parametrized with the following
vector-valued function, r(t) = (t +...
1. A plane curve has been parametrized with the following
vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a.
Carefully make 2 sketches of the plane curve over the interval . (5
pts) b. Compute the velocity and acceleration vectors, v(t) and
a(t). (6 pts) c. On the 1st graph, sketch the position, velocity
and acceleration vectors at t=-1. (5 pts) d. Compute the unit
tangent and principal unit normal vectors, T and N at...
Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5xi+yj−2zk and
C is given by the vector function r(t)=〈sint,cost,t〉,...
Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5xi+yj−2zk and
C is given by the vector function r(t)=〈sint,cost,t〉, 0≤t≤3π/2.