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MATH 230 Final: STAT 230 Amherst S16Stat230Final

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turquoisegnu128

15 Feb 2019

School

Amherst College

Department

Mathematics and Statistics

Course

Professor

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Document Summary

You may not use any calculators or other devices or any notes. Explain answers clearly and completely and show all work in your blue book. Please turn o all devices including cell phones: [20 points] consider the linear map ta : r4 r3, where a is the matrix. 1 1 (a) find a basis for the nullspace null(ta). (b) find a basis for range range(ta): [30 points] de ne the transformation t : m22(r) m22(r) by. 3 4(cid:21) (a) use the properties of matrix multiplication to prove that t is linear. (b) find the matrix of t with respect to the basis. B =(cid:0)e11, e12, e21, e22(cid:1) = (cid:20)1 0. 1 0(cid:21) ,(cid:20)0 0 of m22(r): [30 points] consider the matrix where is a xed scalar. A = (a) assume that 6= 0. Prove that a is not diagonalizable. (b) now assume that = 0. If the general solution to the homogeneous system.

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Related Questions

1) solving the following system of linear equations:

x1+ 2x2 + 3x3 + 4x4 + 5x5= 6

x1+ 2x2 + 4x3 + 3x4 + 7x5= 5

x1+ 2x2 + 2x3 + 5x4 + 4x5= 9

Write the solution in parametric form.

2) Define a function T:R^(3) to R^(2) by T(x,y,z) = (x + y + z,x +2y - 3z)

a) Show that T is a linear transofrmation

b) Find all the vectors in the kernel of T

c) Show that T is onto

d) Find the matrix representation of T relative to the standardbasis of R^(3) and R^(2)

3) Show that B= {(1,1,1), (1,1,0), (0,1,1)} is a basis forR^(3). Find the coordinate vector of (1,2,3) relative to the basisof B.

4) Use the Gram-Schmidt process to find an orthonormal basis forthe subspace of R^(4) spanned by the vectors(1,0,1,1), (1,0,1,0), (0,0,1,1).

5) Consider the Matrix B = {(3,2,-3), (-3,-4,9), (-1,-2,5)}.Find an invertible matrix P and a diagonal matrix D such thatB=PDP^(-1).

ALL WORK AND STEPS MUST BE SHOWN OR YOUR RESPONSE WILL NOT GETRATED!!

I needed help with all of them.

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needed help with 2-6

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