MATRICES Know how to write a Matrix Know

MATRICES 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) Let Maths take you Further… Designed by Victor Help you improve jqwh@bjnewtalent. com

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. COLUMN 1 COLUMN 2 COLUMN 3 COLUMN 4 ROW 1 1 3 5 12 Comparison Row 1 ROW 2 4 5 11 6 Row 2 ROW 3 3 4 7 -5 Row 3 ROW 4 -2 0 13 9 Row n Column 1 Column 2 Column 3 Column n This is a 4 x 4 matrix Because you have 4 rows and 4 columns 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 , Comparison so , Observation 2: ADDMath Designed by Victor Help you improve

SCALAR MULTIPLICATION OF MATRICES Comparison Properties of scalar multiplication 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 Comparison matrix corresponds to a row of A and a column of B. MUST BE SAME SIZE OF PRODUCT ADDMath Designed by Victor Help you improve

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

MULTIPLICATION OF MATRICES properties of matrix multiplication Comparison Given that ADDMath and 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 1 s while the other elements are all 0 s is known as an identity matrix Comparison Example 11 State whether each of the following matrices is an identity matrix: (a) ADDMath (b) (c) Designed by Victor Help you improve

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

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