Quiz

May 10, 2006

Topic: Uses of reduced row echelon form

v_1 = (1, 0, -3, -3, 1) ;

v_2 = (0, 1, 1, 0, 1) ;

v_3 = (-1, 0, 1, 0, -2) ;

1) Is {v_1,v_2,v_3} an independent set?

2) Give a basis of Span{v_1,v_2,v_3} that is orthonormal.

3) Give a basis of ^5 that contains v_1, v_2, and v_3.

4) Give a matrix that has eigenvalues 2, 3, and 5.

5) Give a matrix M with
    M v_1^T =2 v_1^T
and
    M v_2^T =3 v_2^T .

6) Give the eigenvalues and eigenvectors of

    R = ({{2, -1}, {-3, 2}})

Solutions

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