MATH 280 Final: MATH 280 Amherst S18M280Final

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turquoisegnu128

15 Feb 2019

School

Amherst College

Department

Mathematics and Statistics

Course

MATH 280

Professor

All

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Document Summary

Show your work, and justify all your answers. Partial credit will be given for solutions on the right track that might not be complete. Therefore it is recommended that you attempt all prob- lems: [20 points] consider the following matrix a and vector b: If so, express b as a linear combination of the basis vectors you found in part (c): [10 points] let w = span{ . 1 (a) find the eigenvalues and eigenvectors of a. (b) find an orthogonal matrix p such that d = ptap is diagonal. What is d? (c) determine a formula for ak, k n: [20 points] de ne the linear transformation t : r2[x] m22 by c] , Justify your answers. (d) find the matrix representation of t with respect to the bases b = {1, 1 + x, 1 + x + x2} of. 0 1]} of m22: [15 points] let t be the following transformation,

Related Questions

For the matrix A =
1 2 â1 1
3 6 â2 1
â1 â2 3 â5
and the column vector b =
â5
â13
9
(a) Find the reduced row echelon form of the augmented matrix [A|b].
(b) State the rank of A. Is the column space of A a line, a plane, or all of R3? Justify
your answer.
(c) Find the null space of A. Is the null space of A zero, a line, a plane, or all of R3?
Justify your answer.
(d) Find the general solution to the system Ax = b.