MATH 348 - Advanced Engineering Mathematics April 16, 2008
Homework 9, Spring 2008 Due: April 23, 2008
Linear Algebra - Row Reduction and Solutions to Linear Systems
1. Given the linear system
6x1+ 18x2−4x3= 20
−x1−3x2+ 8x3= 4
5x1+ 15x2−9x3= 11.
Determine the general solution to the linear system and describe this set geometrically.
2. Given the following augmented matrix
1 3
3h
2
k.
Determine hand ksuch that the corresponding linear system is :
(a) consistent with a unique solution.
(b) consistent with infinitely many solutions.
(c) inconsistent.
3. Determine if bis a linear combination of the vectors formed from the columns of the matrix A.
A=
5 3
−4 7
9−2
,b=
22
20
15
4. Determine the values of hfor which the vectors are linearly dependent.
v1=
1
−1
−3
,v2=
−5
7
8
,v3=
1
1
h
5. Given,
A=
−8−2−9
648
404
,w=
2
1
−2
.
(a) Is win the column space of A? That is, does w∈Col A?
(b) Is win the null space of A? That is, does w∈Nul A?
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