1. Designed by Victor Help you improve jqwh@bjnewtalent.com MATRICES Let Maths take you Further… Know how to write a Matrix, Know what is Order of Matrices, Addition and Subtraction of Matrices, Multiplication of Matrices, Using Matrices to solve simultaneous equations (Find determinant, Inverse)

2. Comparison ADDMath Designed by Victor Help you improve WHAT IS MATRICES? A matrix is a rectangular array of data entries (elements) displayed in rows and columns and enclosed in brackets, The number of rows and columns in the matrix determines its dimensions. COLUMN1COLUMN2COLUMN3COLUMN4 ROW1 13512 ROW2 45116 ROW3 347-5 ROW4 -20139 This is a 4 x 4 matrix Because you have 4 rows and 4 columns Row 1 Row 2 Row 3 Row n Column1Column2Column3Column n

3. Comparison ADDMath Designed by Victor Help you improve ADDITION & SUBTRACTION of MATRICES To add or subtract 2 or more matrices, we must be sure that we have the same frame. That is, the same number of rows and columns. Given that, so, Observation 2:

4. Comparison ADDMath Designed by Victor Help you improve SCALAR MULTIPLICATION OF MATRICES Properties of scalar multiplication

5. Comparison ADDMath Designed by Victor Help you improve MULTIPLICATION OF MATRICES The multiplication of matrices is easier shown than put into words. You multiply the rows of the first matrix with the columns of the second adding products This figure illustrates diagrammatically the product of two matrices A and B, showing how each intersection in the product matrix corresponds to a row of A and a column of B. MUST BE SAME SIZE OF PRODUCT

6. Comparison ADDMath Designed by Victor Help you improve MULTIPLICATION OF MATRICES (3 × 3) + (4 × 1) = 13(3 × 2) + (4 × 1) = 10 (1 × 2) + (3 × 1) = 5(1 × 2) + (2 × 1) = 4 MUST BE SAME SIZE OF PRODUCT properties of matrix multiplication

7. Comparison ADDMath Designed by Victor Help you improve MULTIPLICATION OF MATRICES properties of matrix multiplication Given that and

8. Comparison ADDMath Designed by Victor Help you improve IDENTITY MATRIX (UNIT MATRIX) A square matrix whose elements along the diagonal from the upper left-hand corner to the bottom right-hand corner are all 1s while the other elements are all 0s is known as an identity matrix Example 11 State whether each of the following matrices is an identity matrix: (a) (b) (c)

9. Comparison ADDMath Designed by Victor Help you improve Solution: a) b)

10. Comparison ADDMath Designed by Victor Help you improve SOLVE SIMULTANEOUS EQUATIONS coefficient matrix variable matrix constant matrix