Fundamentals of Matrix Algebra, 2011a

1.2 Using Matrices To Solve Systems of Linear Equaons
At this stage, we have yet to discuss how to efficiently find a soluon to a system
of linear equaons. That is a goal for the upcoming secons. Right now we focus on
idenfying linear equaons. It is also useful to “limber” up by solving a few systems of
equaons using any method we have at hand to refresh our memory about the basic
process.
Exercises 1.1
In Exercises 1 – 10, state whether or not the
given equaon is linear.
1. x + y + z = 10
2. xy + yz + xz = 1
3. −3x + 9 = 3y − 5z + x − 7
√
4. 5y + πx = −1
5. (x − 1)(x + 1) = 0
√
6. x
2
1 + x 2 2 = 25
7. x 1 + y + t = 1
8.
1
+ 9 = 3 cos(y) − 5z
x
9. cos(15)y + x 4 = −1
10. 2 x + 2 y = 16
In Exercises 11 – 14, solve the system of linear
equaons.
11.
x + y = −1
2x − 3y = 8
12.
13.
14.
2x − 3y = 3
3x + 6y = 8
x − y + z = 1
2x + 6y − z = −4
4x − 5y + 2z = 0
x + y − z = 1
2x + y = 2
y + 2z = 0
15. A farmer looks out his window at his
chickens and pigs. He tells his daughter
that he sees 62 heads and 190 legs.
How many chickens and pigs does the
farmer have?
16. A lady buys 20 trinkets at a yard sale.
The cost of each trinket is either $0.30
or $0.65. If she spends $8.80, how
many of each type of trinket does she
buy?
1.2 Using Matrices To Solve Systems of Linear Equaons
AS YOU READ ...
. . .
1. What is remarkable about the definion of a matrix?
2. Vercal lines of numbers in a matrix are called what?
3. In a matrix A, the entry a 53 refers to which entry?
4. What is an augmented matrix?
In Secon 1.1 we solved a linear system using familiar techniques. Later, we commented
that in the linear equaons we formed, the most important informaon was
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