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Matrices A matrix is a rectangular array that can be used to store information. For example consider the following: Wentport School GCSE results for Mrs Robson’s top set year 11 in 2009 were four A*’s, twenty A’s and 3 B’s. Nearby Rippington School GCSE results for Mr Smith’s top set year 11 for that year were one A*,eighteen A’s and eleven B’s 4203 11811 So the information above has been stored in a 2 x 3 (2 by 3) matrix and we say that it contains 6 elements. The size of the matrix is known as its ORDER and is denoted by the number rows x the number of columns.

Matrices Question 1. By inspecting rows and columns, write down the order of the matrices below. 2 x 4 3 x 2 2 x 2 (square matrix) 4 x 1 (column matrix) 3 x 3 (square matrix) 1 x 3 (row matrix) 2 x 3 3 x 4

Matrices Question 2. Abbey, Claire and Danny sat English, maths and science tests. Abbey scored 67% in English, 48% in maths and 51% in science. Claire scored 72% in English, 84% in maths and 68% in science. Danny scored 90% in English, 52% in maths and 38% in science. Record this information in a suitable matrix. Question 3. On Sunday an electrical store sold eighteen TV’s, twelve iPAD’s, fifteen PC’s and nine printers. On Monday it sold nine TV’s, three iPADS, no PC’s and two printers. On Tuesday it sold four TV’s, two IPAD’s, one PC and sold no printers but had one returned by a customer. Record this information in a suitable matrix.

Matrices Matrices of the same order can be added and subtracted. Consider the earlier matrix (call it m) that recorded information on GCSE results for 2009 below together with the matrix (n) that records the results for 2010. Wentport School GCSE results for Mrs Robson’s top set year 11 in 2009 were four A*’s, twenty A’s and 3 B’s. Nearby Rippington School GCSE results for Mr Smith’s top set year 11 for that year were one A*,eighteen A’s and eleven B’s Wentport School GCSE results for Mrs Robson’s top set year 11 in 2010 were three A*’s, seventeen A’s and five B’s. Nearby Rippington School GCSE results for Mr Smith’s top set year 11 for that year were five A*,eighteen A’s and seven B’s By adding corresponding elements in each matrix we can get the combined totals for both years. 7 378 6 3618 Similarly we could record the difference by subtracting. 1 3 -2 -4 04

Matrices Question 4. Consider the earlier question about the sale of items from an electrical retail outlet together with the matrix m, that records this information. If matrix n records the information for the same three days in the following week write down the matrix that: (a) Combines total sales for both weeks. (b) Shows the difference in sales from week one to week two. On Sunday an electrical store sold eighteen TV’s, twelve iPAD’s, fifteen PC’s and nine printers. On Monday it sold nine TV’s, three iPADS, no PC’s and two printers. On Tuesday it sold four TV’s, two IPAD’s, one PC and sold no printers but had one returned by a customer.

Question 5. Which of the following matrices shown can be added or subtracted to/from matrix M. Matrices

Question 6. Which of the following matrices shown can be added or subtracted to/from matrix P. Matrices

Question 7. Write down the matrix for: (a) a + c (b) b – d (c) c - a Matrices (a) (b) (c)

Worksheet Matrices Question 1. By inspecting rows and columns, write down the order of the matrices below. Question 2. Abbey, Claire and Danny sat English, maths and science tests. Abbey scored 67% in English, 48% in maths and 51% in science. Claire scored 72% in English, 84% in maths and 68% in science. Danny scored 90% in English, 52% in maths and 38% in science. Record this information in a suitable matrix. Question 3. On Sunday an electrical store sold eighteen TV’s, twelve iPAD’s, fifteen PC’s and nine printers. On Monday it sold nine TV’s, three iPADS, no PC’s and two printers. On Tuesday it sold four TV’s, two IPAD’s, one PC and sold no printers but had one returned by a customer. Record this information in a suitable matrix. Question 4. Consider the earlier question about the sale of items from an electrical retail outlet together with the matrix m, that records this information. If matrix n records the information for the same three days in the following week write down the matrix that: (a) Combines total sales for both weeks. (b) Shows the difference in sales from week one to week two. Question 5. Which of the following matrices shown can be added or subtracted to/from matrix M. Question 7. Write down the matrix for: (a) a + c (b) b – d (c) c - a