MACS-332A - Linear Algebra
Homework #1: 1.1 - 1.3
True or False. You must justify your answer.
1. Elementary row operations on an augmented matrix never change the solution set of the associated
linear system.
True - Information preceding the subsection,
MACS-332A - Linear Algebra
Homework #1: 1.3 - 1.5
True or False. You must justify your answer.
1. The weights c1 , . . . , cn in a linear combination c1 v1 + + cn vn cannot all be zero.
False - see page 32 (following the subsection Linear Combinations)
2.
MACS-332A - Linear Algebra
Homework #1: 1.5 - 1.8
True or False. You must justify your answer.
1. The equation x = x2 u + x3 v, with x2 and x3 free (and neither u nor v a multiple of the other), describes a
plane through the origin.
True - see page 51
2.
MACS-332A - Linear Algebra
Homework #4: 1.9, 2.1 - 2.2
True or False. You must justify your answer.
1. The standard matrix of a linear transformation from R2 to R2 that reects points through the horizontal
a0
axis, the vertical axis, or the origin has the
MACS-332A - Linear Algebra
Homework #6: 3.1-3.2, 4.1
True or False. You must justify your answer.
1. The cofactor expansion of detA down a column is the negative of the cofactor expansion along a row.
False: See Theorem 3.1
2. The determinant of a triangu
MACS-332A - Linear Algebra
Homework #7: 4.2-4.4
Due: Wednesday 3/28
True or False. You must justify your answer.
1. The column space of an m n matrix is in Rm .
True. See Theorem 3.
2. N ulA is the kernel of the mapping x Ax.
True. See the paragraph after
MACS 332A - Summer 2007
NAME:
Quiz 2
In order to receive full credit, SHOW ALL YOUR WORK. Full credit will be given only if all reasoning and work
is provided. Please enclose your nal answers in boxes.
1. (12 points) Let
2
4 2 4
1
A = 2 6 3
3
8
2 3
(a) Fi