# 11.5: Matrix Tables and Nested Loops

• • Carey Smith
• Oxnard College
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By Carey A. Smith

A table with 2 or more related rows or columns can be created as a matrix, as shown in these examples.

##### Example $$\PageIndex{1}$$ Row matrix table of squares and cubes

x1 = 13:16
% x1 = 13 14 15 16
x2 = x1.^2 % square each element of x1
% x2 = 169 196 225 256
x3 = x1.^3 % cube each element of x1
% x3 = 2197 2744 3375 4096
% These can be put into a single variable that is a horizontal table relating these values:
x_table = [x1
x2
x3]
% x_table =
% 13 14 15 16
% 169 196 225 256
% 2197 2744 3375 4096

##### Example $$\PageIndex{2}$$ Column matrix table of squares and cubes

%% Often,a vertical table is preferred, especially if there are a lot of values.
y1 = 11:20;
y2 = y1.^2; % square each element of y1
y3 = y1.^3; % cube each element of y1
% A vertical table is created by transposing each horizontal vector into a vertical vector:
y_table = [y1' y2' y3']
% y_table =
% 11 121 1331
% 12 144 1728
% 13 169 2197
% 14 196 2744
% 15 225 3375
% 16 256 4096
% 17 289 4913
% 18 324 5832
% 19 361 6859
% 20 400 8000

##### Example $$\PageIndex{3}$$ km to miles matrix table

%% Example of km to miles
% In this case, each vector is created as a vertical vector, so the transpose is not needed when creating the table:
km = (1:10)' % The ' is the transpose operator.
% km =
% 1
% 2
% 3
% 4
% 5
% 6
% 7
% 8
% 9
% 10
km2miles = 0.6214 % km per mile
miles = km2miles*km
% miles =
% 0.6214
% 1.2428
% 1.8642
% 2.4856
% 3.1070
% 3.7284
% 4.3498
% 4.9712
% 5.5926
% 6.2140
km_2_miles_table = [km miles]
% km_2_miles_table =
% 1.0000 0.6214
% 2.0000 1.2428
% 3.0000 1.8642
% 4.0000 2.4856
% 5.0000 3.1070
% 6.0000 3.7284
% 7.0000 4.3498
% 8.0000 4.9712
% 9.0000 5.5926
% 10.0000 6.2140

##### Exercise $$\PageIndex{1}$$ Even-Odd Nested Loops

Watch this video:

Then code the nested for-loops shown in the video for the even-odd algorithm, with these changes:

1. Delete this line A = input('Please enter an array > '). Instead, code your own 3x4 matrix.

2. Since i is the imaginary number = sqrt(-1), use ii and jj for the loop indices.