# University of Manchester Mathematics Questions

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

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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]

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Tags:
mathematics function

function matrix

coefficient determination

matrix

line intergral

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