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Matrix Operations in Excel

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Matrix Operations in Excel Powered By Docstoc
					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
Matrix Addition
Matrices must be the same size

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

  [B], 3x2         4             8
                   6             1
                   0             5
Matrix Addition
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
Matrix Addition
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
Matrix Addition
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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posted:11/21/2011
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