# Matrix Operations in Excel by linzhengnd

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• pg 1
```									Engineering with Excel, 3rd Ed.
Ron Larsen

DATA SETS
Chapter 5

Intent:     This workbook provides access to the data sets used as examples in the chapter.

Most data sets appear in the text in a figure or table. The figure or table numbers
appear on the worksheet tabs at the bottom of this workbook.
the chapter.

ble numbers
[A], 3x2   1   3
7   2
8   1
Matrices must be the same size

[A], 3x2         1             3
7             2
8             1

[B], 3x2         4             8
6             1
0             5
Matrices must be the same size

[A], 3x2         1             3
7             2
8             1

[B], 3x2         4             8
6             1
0             5

[A] + [B]        5
Matrices must be the same size

[A], 3x2         1             3
7             2
8             1

[B], 3x2         4             8
6             1
0             5

[A] + [B]        5         11
13          3
8          6
Matrices must be the same size

[A], 3x2         1             3   Note: Array name "A" has been limited to this worksheet
7             2   so that it can be used in other examples.
8             1   The Excel default is to set the scope to "workbook".

[B], 3x2         4             8
6             1
0             5

[A] + [B]        5         11
13          3
8          6
Scalar Multiplication

Scalar:        10

[A], 3x2          1   3
7   2
8   1
Scalar Multiplication

Scalar:        10

[A], 3x2          1    3
7    2
8    1

S [A]        10   30
70   20
80   10
Scalar Multiplication - Using Array Math

Scalar:         10

[A], 3x2          1          3
7          2
8          1

S [A]         10         30
70         20
80         10
Matrix Multiplication
Inside dimensions must match (2, 2 in this example)
Product dimensions from outside dimensions (3x1 in this example)

[A], 3x2          1          3
7          2
8          1

[e], 2x1         4
8
Matrix Multiplication
Inside dimensions must match (2, 2 in this example)
Product dimensions from outside dimensions (3x1 in this example)

[A], 3x2         1          3
7          2
8          1

[e], 2x1         4
8

[A][e], 3x1        28
44
40
Matrix Multiplication
Inside dimensions must match (2, 2 in this example)
Product dimensions from outside dimensions (3x4 in this example)

[A], 3x2         1          3
7          2
8          1

[G], 2x4          1          2          3          4
5          6          7          8

[A][G], 3x4        16         20         24         28
17         26         35         44
13         22         31         40
Matrix Transpose
Interchange rows and columns
Any size matrix

[A], 3x2        1      3
7      2
8      1

[A-trans], 2x3        1      7   8
3      2   1
Transpose the following matrices:       Solutions

6          1    4               6
1
4

1        1.2                 1        3
3        6.1               1.2      6.1
4        2.3

1          0    0               1    0
0          1    0               0    1
0          0    1               0    0
4
2.3

0
0
1
Invert a Matrix
Matrix must be square and nonsingular

[J], 3x3        2          3           5
7          2           4
8         11           6

[J-inv], 3x3   -0.1517    0.1754       0.0095
-0.0474   -0.1327       0.1280
0.2891    0.0095      -0.0806
Matrix Determinant
Matrix must be square

[J], 3x3          2    3   5
7    2   4
8   11   6

Det(J)       211
Matrix Determinant
Matrix must be square

[K], 4x4           2    3    5   7   <<< identical
2    3    5   7   <<< rows
8   11    6   4
7    5   12   1

Det(K)            0
Solving Simultaneous Linear Equations

[Coeff]         3          2         4   [rhs]    5
2          5         3           17
7          2         2           11
Solving Simultaneous Linear Equations

[Coeff]         3          2          4    [rhs]        5
2          5          3                17
7          2          2                11

[Coeff-inv]   -0.0513    -0.0513      0.1795     [x]    0.8462
-0.2179     0.2821      0.0128            3.8462
0.3974    -0.1026     -0.1410           -1.3077
Multiloop Circuits I

[Coeff]           1        -1        -1    [rhs]       0
30        40         0               12
30         0        50               12

Determinant:          4700

[Coeff-inv]       0.4255    0.0106    0.0085     [x]   0.2298
-0.3191    0.0170   -0.0064           0.1277
-0.2553   -0.0064    0.0149           0.1021
Wheatstone Bridge I

E:          12 volts
R1 :        20 ohms
R2 :        10 ohms
R4 :        24 ohms
R5 :        100 ohms

R3 :        12 ohms

[Coeff]           1    1    -1   [rhs]    0
30    0   100           12
0   36   100           12

Determinant: -7680

[Coeff-Inv] 0.469 0.02 -0.01          [i] 0.056
0.391 -0.01 0.02             0.047
-0.141     0    0             0.103
Heat Conduction

A         B         C         D         E         F         G         H         I         J         K         L
[Coeff]     A        -4         1         0         0         1         0         0         0         0         0         0         0
B         1        -4         1         0         0         1         0         0         0         0         0         0
C         0         1        -4         1         0         0         1         0         0         0         0         0
D         0         0         1        -4         0         0         0         1         0         0         0         0
E         1         0         0         0        -4         1         0         0         1         0         0         0
F         0         1         0         0         1        -4         1         0         0         1         0         0
G         0         0         1         0         0         1        -4         1         0         0         1         0
H         0         0         0         1         0         0         1        -4         0         0         0         1
I         0         0         0         0         1         0         0         0        -4         1         0         0
J         0         0         0         0         0         1         0         0         1        -4         1         0
K         0         0         0         0         0         0         1         0         0         1        -4         1
L         0         0         0         0         0         0         0         1         0         0         1        -4

[Coeff Inv]       -0.30     -0.10     -0.04     -0.01     -0.10     -0.07     -0.03     -0.01     -0.03     -0.03     -0.02     -0.01
-0.10     -0.34     -0.11     -0.04     -0.07     -0.13     -0.08     -0.03     -0.03     -0.05     -0.04     -0.02
-0.04     -0.11     -0.34     -0.10     -0.03     -0.08     -0.13     -0.07     -0.02     -0.04     -0.05     -0.03
-0.01     -0.04     -0.10     -0.30     -0.01     -0.03     -0.07     -0.10     -0.01     -0.02     -0.03     -0.03
-0.10     -0.07     -0.03     -0.01     -0.33     -0.13     -0.05     -0.02     -0.10     -0.07     -0.03     -0.01
-0.07     -0.13     -0.08     -0.03     -0.13     -0.39     -0.15     -0.05     -0.07     -0.13     -0.08     -0.03
-0.03     -0.08     -0.13     -0.07     -0.05     -0.15     -0.39     -0.13     -0.03     -0.08     -0.13     -0.07
-0.01     -0.03     -0.07     -0.10     -0.02     -0.05     -0.13     -0.33     -0.01     -0.03     -0.07     -0.10
-0.03     -0.03     -0.02     -0.01     -0.10     -0.07     -0.03     -0.01     -0.30     -0.10     -0.04     -0.01
-0.03     -0.05     -0.04     -0.02     -0.07     -0.13     -0.08     -0.03     -0.10     -0.34     -0.11     -0.04
-0.02     -0.04     -0.05     -0.03     -0.03     -0.08     -0.13     -0.07     -0.04     -0.11     -0.34     -0.10
-0.01     -0.02     -0.03     -0.03     -0.01     -0.03     -0.07     -0.10     -0.01     -0.04     -0.10     -0.30
[rhs]   -100
-100
-100
-200
0
0
0
-100
-25
-25
-25
-125

[T]    50.4
(°C)    70.6
81.4
90.2
31.1
50.8
64.7
79.5
23.2
36.6
47.3
62.9
Simultaneous Equations I

Part a.           [C]      3   0   5   [r]   3
8   7   8         8
0   3   7         2

Part b.           [C]      1   2   0   [r]   4
0   1   1         3
2   5   1         3

Part c.           [C]      4   3   3   [r]   7
3   8   4         3
3   2   8         2

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