Quiz

May 10, 2006

Topic: Using reduced row echelon form

Overscript[w_1, _] = ({{1}, {2}, {2}, {1}}), Overscript[w_2, _] = ({{1}, {2}, {2}, {2}}), Overscript[w_3, _] = ({{2}, {2}, {2}, {1}})

1) What is the dimension of Span{Overscript[w_1, _], Overscript[w_2, _],Overscript[w_3, _]}?

2) Find a vector Overscript[u, _] such that {Overscript[w_1, _], Overscript[w_2, _],Overscript[w_3, _], Overscript[u, _]} is a basis of ^4.

Overscript[u, _] = ( {{___}, {___}, {___}, {___}} )

3) Give a 4×4 matrix M with eigenvalues 2, -3, 4, 0, and eigenvectors Overscript[w_1, _], Overscript[w_2, _],Overscript[w_3, _], Overscript[u, _], respectively (in other words, M Overscript[w_1, _]=2Overscript[w_1, _], and so on).

M = ({{___, ___, ___, ___}, {___, ___, ___, ___}, {___, ___, ___, ___}, {___, ___, ___, ___}})

Solutions

Created by Mathematica  (May 15, 2006) Valid XHTML 1.1!