Matrix Solution of Linear Systems
A matrix (plural: matrices) is a rectangular array of numbers arranged in rows and
columns and enclosed in brackets. Each number in the matrix is called an element of
the matrix.
Each of the following is an example of a m

Tutorial 1
Fluid properties
1. A reservoir of glycerin has a mass of 1100kg and a volume of 0.9 m 3. Calculate its weight, mass
density, specific weight and specific gravity.
Solution:
Mass of glycerin (m) = 1100kg
Volume (V) = 0.9 m3
Weight (W) = ?
Mass

The matrices and the properties of matrices
Specific entries of a matrix are often referenced by using pairs of subscripts.
A matrix is a rectangular arrangement of numbers. For example,
An alternative notation uses large parentheses instead of box bracke

Cramer's rule
Cramer's rule is a theorem in linear algebra, which gives an expression for the solution of a system
of linear equations with as many equations as unknowns, valid in those cases where there is unique
solution; this solution is then expressed

1 - Matrices and Systems of Equations
Definition of a Matrix
Rectangular array of real numbers
m rows by n columns
Named using capital letters
First subscript is row, second subscript is column
Terminology
A matrix with m rows and n columns is called a ma

Inverse of Matrices
Requirements to have an Inverse
1. The matrix must be square (same number of rows and columns).
2. The determinant of the matrix must not be zero. This is instead of the real number not being
zero to have an inverse, the determinant mu

Linear Equations: Solutions Using Elimination
Systems of equations with three variables are only slightly
more complicated to solve than those with two variables. The two
most straightforward methods of solving these types of equations
are by elimination

Systems of Linear Equations: Solving by
Substitution
The method of solving "by substitution" works by solving one of the
equations (you choose which one) for one of the variables (you choose which
one), and then plugging this back into the other equation,

Determinants
Determinants are mathematical objects that are very useful in the analysis and solution
of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system
of linear equations has a unique solution iff the determinant of the sy

Solving Systems of Linear Equations Using Matrices
I. Gauss-Jordan Method
A very systematic method of solving linear systems of equations is called the
Gauss—Jordan Method. This method involves the use of matrices, the plural of the
word matrix. A matrix

Tutorial 5
Relative equilibrium
1. An open rectangular tank 3m long and 2m wide is filled with water to a depth of 1.5m. Find the slope
of the water surface when the tank moves with an acceleration of 5m/s2 up a 300 inclined plane. Also
calculate the pres