Java Reference
In-Depth Information
In order to be added, the two matrices must have the same dimensions and the
same or compatible types of elements. Let
c
be the resulting matrix. Each ele-
ment
c
ij
is
a
ij
+
b
ij
. For example, for two 3
*
3 matrices
a
and
b
,
c
is
£
a
11
a
12
a
13
£
b
11
b
12
b
13
£
a
11
+
b
11
a
12
+
b
12
a
13
+
b
13
a
21
a
22
a
23
≥
+
b
21
b
22
b
23
≥
=
a
21
+
b
21
a
22
+
b
22
a
23
+
b
23
≥
VideoNote
Multiply two matrices
a
31
a
32
a
33
b
31
b
32
b
33
a
31
+
b
31
a
32
+
b
32
a
33
+
b
33
Write a test program that prompts the user to enter two 3
*
3 matrices and
displays their sum. Here is a sample run:
Enter matrix1: 1 2 3 4 5 6 7 8 9
Enter matrix2: 0 2 4 1 4.5 2.2 1.1 4.3 5.2
The matrices are added as follows
1.0 2.0 3.0 0.0 2.0 4.0 1.0 4.0 7.0
4.0 5.0 6.0 + 1.0 4.5 2.2 = 5.0 9.5 8.2
7.0 8.0 9.0 1.1 4.3 5.2 8.1 12.3 14.2
**8.6
(
Algebra: multiply two matrices
) Write a method to multiply two matrices. The
header of the method is:
public static double
[][]
multiplyMatrix(
double
[][] a,
double
[][] b)
To multiply matrix
a
by matrix
b
, the number of columns in
a
must be the same as
the number of rows in
b
, and the two matrices must have elements of the same or
compatible types. Let
c
be the result of the multiplication. Assume the column size
of matrix a is
n
. Each element
c
ij
is
a
i
1
*
b
1
j
+
a
i
2
*
b
2
j
+ c +
a
in
*
b
nj
.
For example, for two 3
*
3 matrices
a
and
b
,
c
is
£
a
11
a
12
a
13
£
b
11
b
12
b
13
£
c
11
c
12
c
13
a
21
a
22
a
23
≥
*
b
21
b
22
b
23
≥
=
c
21
c
22
c
23
≥
a
31
a
32
a
33
b
31
b
32
b
33
c
31
c
32
c
33
where
c
ij
=
*
+
*
+
*
a
i
1
b
1
j
a
i
2
b
2
j
a
i
3
b
3
j
.
*
Write a test program that prompts the user to enter two 3
3 matrices and dis-
plays their product. Here is a sample run:
Enter matrix1: 1 2 3 4 5 6 7 8 9
Enter matrix2: 0 2 4 1 4.5 2.2 1.1 4.3 5.2
The multiplication of the matrices is
1 2 3 0 2.0 4.0 5.3 23.9 24
4 5 6 * 1 4.5 2.2 = 11.6 56.3 58.2
7 8 9 1.1 4.3 5.2 17.9 88.7 92.4
*8.7
(
Points nearest to each other
) Listing 8.3 gives a program that finds two points in a
two-dimensional space nearest to each other. Revise the program so that it finds two
points in a three-dimensional space nearest to each other. Use a two-dimensional
array to represent the points. Test the program using the following points:
double
[][] points = {{
-1
,
0
,
3
}, {
-1
,
-1
,
-1
}, {
4
,
1
,
1
},
{
2
,
0.5
,
9
}, {
3.5
,
2
,
-1
}, {
3
,
1.5
,
3
}, {
-1.5
,
4
,
2
},
{
5.5
,
4
,
-0.5
}};
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