Get help with vectors and spaces

Suppose$U=\{(x,y,x+y,x-y,2x)\in F^5,x,y\in F\}$ . Find a subspace $W$of $F^5$ such that $F^5=U\oplus W$.

For any vectors u, v and w, show that the vectors u+v, u+w and v+w form a linearly dependent set.

Write in words how to read each of the following:

{x∈I ├|0<x<1┤}

{x∈R├|x≤0 or x≥1┤}

The symmetric difference of A and B, denoted by A B, is the set containing those elements in 
either A or B, but not in both A and B.
a) Find the symmetric difference o f { 1, 3 , 5 } and { 1, 2, 3 } .
b) Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it follow that
A (B C) = (A B) C?

If u, v, w ∈ R n , then span(u, v + w) = span(u + v, w)

If u, v, w ∈ R n , then span(u, v + w) = span(u + v, w)

Determine the average value of F(x, y, z) = xyz throughout the cubical region D
bounded by the coordinate planes and the planes x = 2, y − 2, z = 2 in the first octant.

vv

A second hand car dealer has ten cars for sale. He decides to investigate the link between the

ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars

are shown in the table below.

Age, x years

2 2.5 3 4 4.5 4.5 5 3 6 6.5

Mileage, y thousand miles

22 34 33 37 40 45 49 30 58 58

(a) Construct a well labeled scatter diagram in the graph paper provided to present the

information. (3 marks)

(b) Find Sxx and Sxy. (3 marks)

(c) Find the regression equation in the form y = α + βx. (4 marks)

(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line

appropriately. (2 marks)

(e) Give a practical interpretation of the slope β. (1 mark)

(f) Using your answer in (c), fifind the mileage for a 6 year old car.

A second hand car dealer has ten cars for sale. He decides to investigate the link between the

ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars

are shown in the table below.

Age, x years

2 2.5 3 4 4.5 4.5 5 3 6 6.5

Mileage, y thousand miles

22 34 33 37 40 45 49 30 58 58

(a) Construct a well labeled scatter diagram in the graph paper provided to present the

information. (3 marks)

(b) Find Sxx and Sxy. (3 marks)

(c) Find the regression equation in the form y = α + βx. (4 marks)

(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line

appropriately. (2 marks)

(e) Give a practical interpretation of the slope β. (1 mark)

(f) Using your answer in (c), fifind the mileage for a 6 year old car.

A second hand car dealer has ten cars for sale. He decides to investigate the link between the

ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars

are shown in the table below.

Age, x years

2 2.5 3 4 4.5 4.5 5 3 6 6.5

Mileage, y thousand miles

22 34 33 37 40 45 49 30 58 58

(a) Construct a well labeled scatter diagram in the graph paper provided to present the

information. (3 marks)

(b) Find Sxx and Sxy. (3 marks)

(c) Find the regression equation in the form y = α + βx. (4 marks)

(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line

appropriately. (2 marks)

(e) Give a practical interpretation of the slope β. (1 mark)

(f) Using your answer in (c), fifind the mileage for a 6 year old car

Find the expected count and the contribution to the chi-square statistic for the (Treatment, Disagree) cell in the two-way table below.