Linear algebra questions and answers

Recent questions in Linear algebra
2022-03-09 Answered

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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

Finding detailed linear algebra problems and solutions has always been difficult because the textbooks would never provide anything that would be sufficient. Since it is used not only by engineering students but by anyone who has to work with specific calculations, we have provided you with a plethora of questions and answers in their original form. It will help you to see some logic as you are solving complex numbers and understand the basic concepts of linear Algebra in a clearer way. If you need additional help or would like to connect several solutions, compare more than one solution as you approach your task.