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Matrices

A large number of engineering problems require

the solution of large numbers of equations.

These equations are often manipulated in matrix

form.

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The dot product is the basic arithmetic operation

in matrix algebra

Row Vector

Column Vector

Matrices can be multiplied if the first matrix

contains the same number of columns as the second

has rows. Dot products are formed from the row

vectors of the first matrix and column vectors of

the second.

3 X 2

4 X 2

4 X 3

Linear matrix equations can be solved by finding

the inverse of the coefficient matrix and

multiplying it by the right-hand side column

vector.

Excel can perform matrix calculations, called

array formulas. Matrix calculations in Excel are

cumbersome

- Matrices are defined as cell ranges using a colon

to separate the upper left and lower right cells - Excel array functions are used to perform

calculations - If calculation produces an array result the cell

area containing the result must be pre-selected - Control-Shift-Enter must be pressed to execute

array functions

MMULT()

MINVERSE()

Excel Example

Matlab is a calculation/programming application

that simplifies the manipulation of matrix

equations

- Matrices are entered directly at a command-line

prompt - Matlab functions work directly on matrices

without any special key sequences - Matlab automatically creates matrices of correct

size to store calculation results

MATLAB Example