Linear Algebra 1. Consider the points (1, 2), (2, 3.5), (3, 6.2), which are not on a straight line. Assume that there is a relationship of the form y=mx+b. (a) Write a set of equations, in m and b, by substituting the values of x and y into this relationship. Write this system in matrix form. (b) Use the alternative form of the pseudoinverse ( A* =(A' A)° A' ) to calculate the coefficients m,b. You should use the Excel file on Moodle to perform your calculations. Make sure you change the A matrix and the B vector. The spreadsheet will perform all other calculations for you. (Note that the cells you should enter have colour backgrounds, and the solution cell has text in red.) (c) Give the equation relating x and y for this data.
Linear Algebra 1. Consider the points (1, 2), (2, 3.5), (3, 6.2), which are not on a straight line. Assume that there is a relationship of the form y=mx+b. (a) Write a set of equations, in m and b, by substituting the values of x and y into this relationship. Write this system in matrix form. (b) Use the alternative form of the pseudoinverse ( A* =(A' A)° A' ) to calculate the coefficients m,b. You should use the Excel file on Moodle to perform your calculations. Make sure you change the A matrix and the B vector. The spreadsheet will perform all other calculations for you. (Note that the cells you should enter have colour backgrounds, and the solution cell has text in red.) (c) Give the equation relating x and y for this data.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Linear Algebra
1. Consider the points (1, 2), (2, 3.5), (3, 6.2), which are not on a straight line. Assume that
there is a relationship of the form y= mx+b.
(a) Write a set of equations, in m and b, by substituting the values of x and y into this
relationship. Write this system in matrix form.
(b) Use the alternative form of the pseudoinverse ( A* =(A' A)¨ A' ) to calculate the
coefficients m,b. You should use the Excel file on Moodle to perform your
calculations. Make sure you change the A matrix and the B vector. The spreadsheet
will perform all other calculations for you. (Note that the cells you should enter have
colour backgrounds, and the solution cell has text in red.)
(c) Give the equation relating x and y for this data.
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