Practice and Problem-Solving Exercises
A Practice
See Problem 1.
Identify the indicated element.
A
=
[
3
12
6
1
0
9
8
7
4
]
eh equals . matrix with 3 rows and 3 columns , row1 column 1 , 3 , column 2 12 , column 3 6 , row2 column 1 , 1 , column 2 0 , column 3 9 , row3 column 1 , 8 , column 2 7 , column 3 4 , end matrix
-
a
32
eh sub 32
-
a
21
eh sub 21
-
a
13
eh sub 13
-
a
31
eh sub 31
See Problem 2.
Write a matrix to represent each system.
-
{
x
+
2
y
=
11
2
x
+
3
y
=
18
left brace . table with 2 rows and 3 columns , row1 column 1 , x plus , column 2 2 y equals , column 3 11 , row2 column 1 , 2 x plus , column 2 3 y equals , column 3 18 , end table
-
{
3
x
+
2
y
=
16
y
=
5
left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus 2 y equals 16 , row2 column 1 , y equals 5 , end table
-
{
2
a
−
3
b
=
6
a
+
b
=
2
left brace . table with 2 rows and 3 columns , row1 column 1 , 2 eh minus , column 2 3 b equals , column 3 6 , row2 column 1 , eh plus , column 2 b equals , column 3 2 , end table
-
{
r
−
s
+
t
=
150
2
r
+
t
=
425
s
+
3
t
=
0
left brace . table with 3 rows and 1 column , row1 column 1 , r minus s plus t equals 150 , row2 column 1 , 2 r plus t equals 425 , row3 column 1 , s plus 3 t equals 0 , end table
-
{
y
=
3
x
−
7
x
=
2
left brace . table with 2 rows and 1 column , row1 column 1 , y equals 3 x minus 7 , row2 column 1 , x equals 2 , end table
-
{
x
−
y
+
z
=
0
x
−
2
y
−
z
=
5
2
x
−
y
+
2
z
=
8
left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 y plus , column 3 z equals , column 4 0 , row2 column 1 , x minus , column 2 2 y minus , column 3 z equals , column 4 5 , row3 column 1 , 2 x minus , column 2 y plus , column 3 2 z equals , column 4 8 , end table
See Problem 3.
Write the system of equations represented by each matrix.
-
[
1
0
4
0
1
−
6
]
. matrix with 2 rows and 3 columns , row1 column 1 , 1 , column 2 0 , column 3 4 , row2 column 1 , 0 , column 2 1 , column 3 negative 6 , end matrix
-
[
5
1
−
3
−
2
2
4
]
. matrix with 2 rows and 3 columns , row1 column 1 , 5 , column 2 1 , column 3 negative 3 , row2 column 1 , negative 2 , column 2 2 , column 3 4 , end matrix
-
[
−
1
2
−
6
1
1
7
]
. matrix with 2 rows and 3 columns , row1 column 1 , negative 1 , column 2 2 , column 3 negative 6 , row2 column 1 , 1 , column 2 1 , column 3 7 , end matrix
-
[
2
1
1
1
1
1
1
2
1
−
1
1
−
2
]
. matrix with 3 rows and 4 columns , row1 column 1 , 2 , column 2 1 , column 3 1 , column 4 1 , row2 column 1 , 1 , column 2 1 , column 3 1 , column 4 2 , row3 column 1 , 1 , column 2 negative 1 , column 3 1 , column 4 negative 2 , end matrix
-
[
0
1
2
4
−
2
3
6
9
1
0
1
3
]
. matrix with 3 rows and 4 columns , row1 column 1 , 0 , column 2 1 , column 3 2 , column 4 4 , row2 column 1 , negative 2 , column 2 3 , column 3 6 , column 4 9 , row3 column 1 , 1 , column 2 0 , column 3 1 , column 4 3 , end matrix
-
[
5
2
1
5
4
1
2
8
1
3
−
6
2
]
. matrix with 3 rows and 4 columns , row1 column 1 , 5 , column 2 2 , column 3 1 , column 4 5 , row2 column 1 , 4 , column 2 1 , column 3 2 , column 4 8 , row3 column 1 , 1 , column 2 3 , column 3 negative 6 , column 4 2 , end matrix
See Problems 4 and 5.
Solve the system of equations using a matrix.
-
{
x
+
3
y
=
5
x
+
4
y
=
6
left brace . table with 2 rows and 3 columns , row1 column 1 , x plus , column 2 3 y equals , column 3 5 , row2 column 1 , x plus , column 2 4 y equals , column 3 6 , end table
-
{
p
−
3
q
=
−
1
−
5
p
+
16
q
=
5
left brace . table with 2 rows and 3 columns , row1 column 1 , p minus , column 2 3 q equals , column 3 negative 1 , row2 column 1 , negative 5 p plus , column 2 16 q equals , column 3 5 , end table
-
{
300
x
−
y
=
130
200
x
+
y
=
120
left brace . table with 2 rows and 3 columns , row1 column 1 , 300 x minus , column 2 y equals , column 3 130 , row2 column 1 , 200 x plus , column 2 y equals , column 3 120 , end table
-
{
x
+
3
y
=
22
2
x
−
y
=
2
left brace . table with 2 rows and 3 columns , row1 column 1 , x plus , column 2 3 y equals , column 3 22 , row2 column 1 , 2 x minus , column 2 y equals , column 3 2 , end table
-
{
x
+
3
y
=
6
2
x
+
4
y
=
12
left brace . table with 2 rows and 3 columns , row1 column 1 , x plus , column 2 3 y equals , column 3 6 , row2 column 1 , 2 x plus , column 2 4 y equals , column 3 12 , end table
-
{
x
+
y
=
5
−
2
x
+
4
y
=
8
left brace . table with 2 rows and 3 columns , row1 column 1 , x plus , column 2 y equals , column 3 5 , row2 column 1 , negative 2 x plus , column 2 4 y equals , column 3 8 , end table
