TOPICS
MATRIX, VECTOR
AND MATRIX
ALGEBRA
SCALAR, VECTOR AND MATRIX
A scalar is a number. Examples of scalars are
temperature, distance, speed, or mass – all quantities that
have a magnitude but no “direction”, other than perhaps
positive or negative.
Matrix is a rectangular collection of variables or scalars
contained with a set of square [ ] or round ( ) brackets. A
matrix is consist of m rows and n columns.
SCALAR, VECTOR AND MATRIX
 A vector is a list of numbers. There are (at least) two ways to
interpret what this list of numbers mean: One way to think of the
vector as being a point in a space. Then this list of numbers is a
way of identifying that point in space, where each number
represents the vector’s component that dimension. Another way to
think of a vector is a magnitude and a direction, e.g. a quantity like
velocity (“the fighter jet’s velocity is 250 mph north-by-northwest”).
In this way of think of it, a vector is a directed arrow pointing from
the origin to the end point given by the list of numbers.
SCALAR, VECTOR AND MATRIX
Matrix is a rectangular collection of variables or scalars
contained with a set of square [ ] or round ( ) brackets. A
matrix is consist of m rows and n columns.
IN SIMPLE ......
CLASSIFICATION OF MATRIX
SQUARE MATRIX
DIAGONAL MATRIX
CLASSIFICATION OF MATRIX
INDENTITY MATRIX
SCALAR MATRIX
EQUALITY OF MATRIX
TWO MATRICES ARE EQUAL IF THEY HAVE THE
SAME NUMBER OF ROWS AND COLUMNS AND THEIR
CORRESPONDING ENTRIES ARE ALSO EQUAL.
ADDITION AND SUBTRACTION OF MATRIX
Addition (or subtraction) of two matrices can be
accomplished by adding ( or subtracting) the corresponding
entries of two matrices which have the same shape.
MULTIPLICATION OF MATRIX
Multiplication of matrix can be done only if the numer of
columnc of the left-hand is matrix is equal to the number of
rows of the right-hand matrix.
Multiplication is accomplihed by multiplying the elements in
each right-hand matrix column, adding their products, then
placing the sum at the intersection point of the involved row
and column
DIVISION OF MATRIX
Division of matrices can be accomplished only by
multiplying the inverse of the denominator matrix.
THE DETERMINANT OF A MATRIX
The determinant D, is a scalar calculated from a square
matrix. The determinant of a matrix is indicated by
enclosing the matrix by vertical lines.
PROPERTIES OF DETERMINANTS
A. If a matrix has a row or
column of zeros, the
determinant is zero.
B. If a matrix has two
identical rows or
columns, the determinant
is zero.
C. If a matrix is triangular,
the determininant is
equal to the product of
the diagonal entries
PROPERTIES OF DETERMINANTS
C. If a matrix is triangular,
the determininant is
equal to the product of
the diagonal entries
D. The value of the
determinant is not changed if
corresponding rows and
columns are changed
PROPERTIES OF DETERMINANTS
E. if each of a column or
row of a determinant is
multiplied by m, the value
of the determinant is
multiplied by m.
F. If teo columns or rows of a
deteminant are interchanged
the sign is changed
PROPERTIES OF DETERMINANTS
G. The value of a determinant is not changed if each
element of a column or row is multiplied by a number k and
added or subtracted to the corresponding elements of a
column or row.
MINORS AND CO FACTORS
CALCULATING DETERMINANTS
example