Math 205 Quiz 2
Name:
1. A=
123
234
345
(a) Solve the equation A~x =~
0. Write the answer in vector parameter form.
(b) Using (a), are the columns of Alinearly independent or dependent? If they are dependent, find
some c1, c2, c3(not all zero) such that c1~a1+c2~a2+c3~a3= 0
2. B=1a
−1bFor what values of a,b will the columns of B span R2?
3. Build a matrix (choose numbers m and n and fill in the matrix) to demonstrate the following:
(a) An m by n matrix whose columns are linearly independent but do not span Rm.
(b) An m by n matrix which spans Rmbut whose columns are not linearly independent.
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