University of Manchester Mathematics Questions

Description

i need help with the following two questions, can you please provide solutions with workings

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2

Unformatted Attachment Preview

7. A matrix A is given by
A-[ : 3)
(a) Find 1 and 12, the eigenvalues of A, and find X, and X2, their corres-
ponding eigenvectors.
[7 marks]
(b) State the Trace of A and the determinant of A, and use the properties of
eigenvalues to explain their relationship to the eigenvalues of A.
[3 marks]
3
8. (a) Evaluate the line integral
$. *2 – ydy,
where C is the path starting from (0,0) and ending at (1,1) along the curve
given by
y=r?
[4 marks]
(b) Evaluate the line integral
F. dr,
where
F = (2x – y)i + (x + 3y)j, dr = dxi + dyj,
and C is the path starting from (0,1) and ending at (1,5) along the straight
line given by
y = 4x + 1.
[6 marks]

Purchase answer to see full
attachment

Tags:
mathematics function

function matrix

coefficient determination

matrix

line intergral

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.