Tuesday , December 6 2016
Revision Notes

Matrices

In Mathematics, matrices are arrays of numbers arranged in rows and columns.

Types of Matrices:

Row Matrix:

Capture24

Coloumn Matrix:

Capture26

Special Matrix:

Capture27

Null Matrix (0):

Null Matrix is that matrix, that only contains number 0 in it.

Capture30b

Diagonal Matrix:

Also known as square matrix, in which all element zero except the diagonal upper left to lower left.

Capture31

Identity (or unit) Matrix (I):

The elements in the diagonal are one’s only.

Capture32

Writing the order of Matrices:

Order = Number of Rows *  Number of Columns

Example:

Capture29

Order = 3*2

Capture30

Order = 2 * 3

Addition and Subtraction of Matrices:

Matrices of the same order are added (or subtracted) by adding (or subtracting)  the corresponding elements in each matrix.

Capture33

Adding A + B:                     Subtracting A – B:

Capture34 Capture35

 

Rules:

A+B = B+A : A and B can change position when adding.

(A+B) + C = A + (B+C): order of operation bracket first.

A – B ≠ B –A:  A and B should not change positions when subtracting.

Example:

Capture36

Scaler Multiplication of a Matrix by a real number:

Capture37

Example:

Capture38

Equal Matrix:

If two matrices A and B are of the same order and their corresponding elements are equal, then A = B.

Example:

Capture39

Multiplication of Two or More Matrices:

Matrices can only be multiplied only if they are compatible. They are compatible when the number of rows of the second matrix is the same as the number of coloumns of the first matrix.

Rules:

AB ≠ BA : A and B should not change positions

(AB)C = A(BC): If 3 or more matrices you can choose whichever 2 to    multiply first.

Example:

Capture40

Inverse Of Matrix:

Capture42

Determinant A  = ad – bc

A-1 = Capture43b

Remember:

  • If Determinant = 0 then the matrix has no inverse.
  • Multipying by the inverse of the inverse of a matrix gives the same result as dividing by the matrix.

E.g.

If AB = C

A-1AB = A-1C

B= A1C

Example of Inverse of Matrix:

  • If Determinant = 0 then matrix has no inverse.
  • Multipying by the inverse of the inverse of a matrix gives the same result as dividing by the matrix.

E.g.

Capture44

Example:

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