Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

18.5 Matrix Algebra 607

The diagonal along which values 5, 7, 4, and 11 lies is called theprincipal diagonal. Anidentity

orunit matrixis a diagonal matrix whose elements consist of a value of 1. An example of an iden-

tity matrix follows.

Matrix Addition or Subtraction

Two matrices can be added together or subtracted from each other provided that they are

of the same size — each matrix must have the same number of rows and columns. We can add

matrix [A]mnof dimensionmbyn(havingmrows andncolumns) to matrix [B]mnof the

same dimension by adding the like elements. Matrix subtraction follows a similar rule, as shown.

Matrix Multiplication

In this section, we will discuss the rules for multiplying a matrix by a scalar quantity and by

another matrix.

Multiplying a Matrix by a Scalar Quantity When a matrix [A] is multiplied by a scalar quantity with a mag-

nitude such as 5, the operation results in a matrix of the same size, whose elements are the prod-

uct of elements in the original matrix and the scalar quantity. For example, when we multiply

matrix [A] of size 3 3 by a scalar quantity 5, this operation results in another matrix of size

E

110  2213  122 .. 12  82

15  1211  72 .. 10  152

.....

.....

19  4212  552 .. 17  102

U

3 A 4  3 B 4 E

103..2

51..0

. ....
. ....

92..7

UE

212.. 8

1 7..15

. ....
. ....

455..10

U

3 I 4 G

100..00

010..00

001..00

.......

.......

000..10

000..01

W

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