Practice and Problem-Solving Exercises
A Practice
See Problem 1.
Find each sum or difference.
-
[
5
4
3
1
−
2
6
]
+
[
1
1
1
1
1
1
]
left bracket . table with 2 rows and 3 columns , row1 column 1 , 5 , column 2 4 , column 3 3 , row2 column 1 , 1 , column 2 negative 2 , column 3 6 , end table . right bracket plus left bracket . table with 2 rows and 3 columns , row1 column 1 , 1 , column 2 1 , column 3 1 , row2 column 1 , 1 , column 2 1 , column 3 1 , end table . right bracket
-
[
2
1
2
1
2
1
]
+
[
2
3
2
3
2
3
]
left bracket . table with 2 rows and 3 columns , row1 column 1 , 2 , column 2 1 , column 3 2 , row2 column 1 , 1 , column 2 2 , column 3 1 , end table . right bracket plus left bracket . table with 2 rows and 3 columns , row1 column 1 , 2 , column 2 3 , column 3 2 , row2 column 1 , 3 , column 2 2 , column 3 3 , end table . right bracket
-
[
6.4
−
1.9
−
6.4
0.8
]
+
[
−
2.5
−
0.4
5.8
8.3
]
left bracket . table with 2 rows and 2 columns , row1 column 1 , 6.4 , column 2 negative 1.9 , row2 column 1 , negative 6.4 , column 2 0.8 , end table . right bracket plus left bracket . table with 2 rows and 2 columns , row1 column 1 , negative 2.5 , column 2 negative 0.4 , row2 column 1 , 5.8 , column 2 8.3 , end table . right bracket
-
[
1.5
−
1.9
0
4.6
]
−
[
8.3
−
3.2
2.1
5.6
]
left bracket . table with 2 rows and 2 columns , row1 column 1 , 1.5 , column 2 negative 1.9 , row2 column 1 , 0 , column 2 4.6 , end table . right bracket minus left bracket . table with 2 rows and 2 columns , row1 column 1 , 8.3 , column 2 negative 3.2 , row2 column 1 , 2.1 , column 2 5.6 , end table . right bracket
See Problem 2.
Solve each matrix equation.
-
[
1
2
2
1
−
3
4
]
+
X
=
[
5
−
6
1
0
8
5
]
left bracket . table with 3 rows and 2 columns , row1 column 1 , 1 , column 2 2 , row2 column 1 , 2 , column 2 1 , row3 column 1 , negative 3 , column 2 4 , end table . right bracket plus x equals left bracket . table with 3 rows and 2 columns , row1 column 1 , 5 , column 2 negative 6 , row2 column 1 , 1 , column 2 0 , row3 column 1 , 8 , column 2 5 , end table . right bracket
-
[
2
1
−
1
0
2
1
]
−
X
=
[
11
3
−
13
15
−
9
8
]
left bracket . table with 2 rows and 3 columns , row1 column 1 , 2 , column 2 1 , column 3 negative 1 , row2 column 1 , 0 , column 2 2 , column 3 1 , end table . right bracket minus x equals left bracket . table with 2 rows and 3 columns , row1 column 1 , 11 , column 2 3 , column 3 negative 13 , row2 column 1 , 15 , column 2 negative 9 , column 3 8 , end table . right bracket
-
X
−
[
1
4
−
2
3
]
=
[
5
−
2
1
0
]
x minus left bracket . table with 2 rows and 2 columns , row1 column 1 , 1 , column 2 4 , row2 column 1 , negative 2 , column 2 3 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 5 , column 2 negative 2 , row2 column 1 , 1 , column 2 0 , end table . right bracket
-
X
+
[
6
1
−
2
3
]
=
[
2
0
−
3
1
]
x plus left bracket . table with 2 rows and 2 columns , row1 column 1 , 6 , column 2 1 , row2 column 1 , negative 2 , column 2 3 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 2 , column 2 0 , row2 column 1 , negative 3 , column 2 1 , end table . right bracket
See Problem 3.
Find each sum.
-
[
2
−
3
4
5
6
−
7
]
+
[
0
0
0
0
0
0
]
left bracket . table with 2 rows and 3 columns , row1 column 1 , 2 , column 2 negative 3 , column 3 4 , row2 column 1 , 5 , column 2 6 , column 3 negative 7 , end table . right bracket plus left bracket . table with 2 rows and 3 columns , row1 column 1 , 0 , column 2 0 , column 3 0 , row2 column 1 , 0 , column 2 0 , column 3 0 , end table . right bracket
-
[
6
−
3
−
7
2
]
+
[
−
6
3
7
−
2
]
left bracket . table with 2 rows and 2 columns , row1 column 1 , 6 , column 2 negative 3 , row2 column 1 , negative 7 , column 2 2 , end table . right bracket plus left bracket . table with 2 rows and 2 columns , row1 column 1 , negative 6 , column 2 3 , row2 column 1 , 7 , column 2 negative 2 , end table . right bracket
See Problem 4.
Find the value of each variable.
-
[
2
2
−
1
6
]
−
[
4
−
1
0
5
]
=
[
x
y
−
1
z
]
left bracket . table with 2 rows and 2 columns , row1 column 1 , 2 , column 2 2 , row2 column 1 , negative 1 , column 2 6 , end table . right bracket minus left bracket . table with 2 rows and 2 columns , row1 column 1 , 4 , column 2 negative 1 , row2 column 1 , 0 , column 2 5 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , x , column 2 y , row2 column 1 , negative 1 , column 2 z , end table . right bracket
-
[
2
4
8
4.5
]
=
[
4
x
−
6
−
10
t
+
5
4
x
15
t
+
1.5
x
]
left bracket . table with 2 rows and 2 columns , row1 column 1 , 2 , column 2 4 , row2 column 1 , 8 , column 2 4.5 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 4 x minus 6 , column 2 negative 10 t plus 5 , row2 column 1 , 4 x , column 2 15 t plus 1.5 x , end table . right bracket
