MATH 272 Final: MATH 272 Amherst Math22FinalExam

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turquoisegnu128

15 Feb 2019

School

Amherst College

Department

Mathematics and Statistics

Course

MATH 272

Professor

All

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Document Summary

You may not use any calculators or other devices or any notes. Spring 2009: (20pt) consider the matrix a = If so, write down the general solution of ax=b. Show that if c-i is idempotent, then c is invertible: (20pt) consider the linear transformation t : p. Is t invertible? (c) find the matrix representation of t relative to the bases b={1-t,1+3t,2t-t2} 0 1 for the domain and c = Math 22 final exam: (15pt) show that the matrix a = 4 1 diagonal matrix d similar to a. Then use this information to find a formula for a k involving the eigenvalues of a, where k is a positive integer: (10pt) let a = 0 for positive integers k, a k = K: (10pt) find the line that best fits the data points (0,0), (1,2), and (3,3), (10pt) let a be an nxn matrix.

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.

11 please