104 Quiz LA-01
Name:
SID#
1. True and False (Justify your answer by given a logical argument or a counterexample).
(a) x  y  1 c an be represented geometrically as a plane through the origin in
2-dimention space.
1
0


(b) All linear combination of the vector A  0 and B   2 can fill a plane of a
 
 
0
 0 
3-dimention space.
(c) Multiplication of matrices, whenever defined, is commutative.
(d) The multiplication of an n  n and an m m matrices is an n  m matrix.
(e) If rows 1 and 3 of A are the same, so are rows 1 and 3 of AB.
(f) The equations
2x  3 y  0
can’t be solved in the point of view of column picture.
3x  5 y  0
(g) Suppose that w is a solution to Ax = b, where b
k(u + w) is a solution to Ax =b.
0, and u is a solution to Ax = 0. Then
2. Consider the following linear equations Ax=b,
(a) Find the elimination matrices E21 , E31 , E41 E32 , E42 and E43 that produce the following
matrix A to an upper triangular matrix U. (20%)
(b) Find the solution, if the unique solution exists. (10%)
 2 1
1
2
Ax  
 2 0

3
6
0 2
0 

0 
1 2
x 
0 
1 0

 
0 3
1
計算題點名 2-(a) TA: U0321104
2-(b) TA: U0321142