Matrices

1
Matrices
2
A large number of engineering problems require
the solution of large numbers of equations.
These equations are often manipulated in matrix
form.
?
3
The dot product is the basic arithmetic operation
in matrix algebra
Row Vector
Column Vector
4
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
5
Linear matrix equations can be solved by finding
the inverse of the coefficient matrix and
multiplying it by the right-hand side column
vector.
6
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()
7
Excel Example
8
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

9
MATLAB Example