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© Boardworks Ltd 20132 of 8 What is a matrix? A matrix (plural matrices) is a rectangular array of numbers, displayed in rows and columns inside a large set of brackets. One use of matrices is to organise data clearly. For example, the number of people that attended an exhibition over one weekend can be arranged in a matrix. This is a 3 × 2 (“3 by 2”) matrix because it has 3 rows and 2 columns. It contains 6 elements or entries. Men129105 SaturdaySunday Women10399 Children8067 129105 10399 8067
© Boardworks Ltd 20133 of 8 Adding matrices Two matrices can be added or subtracted if they have the same dimensions. For example: 65 –213 8–17 + 6 + 125 + 4 –2 + 113 – 3 8 + 2–17 + 0 = 124 1–3 20 Add each corresponding element from both matrices to get the resulting element. = 189 –110 –17
© Boardworks Ltd 20134 of 8 Adding and subtracting matrices
© Boardworks Ltd 20135 of 8 Multiplying by a scalar A matrix can be multiplied by a single value (a scalar). Simply multiply each entry in the matrix by that scalar to get the resulting matrix. For example: Calculate: 3 75 32 111 = 7 × 35 × 3 3 × 32 × 3 11 × 31 × 3 = 2115 96 333 5 32 111 – 12 32 = 1510 555 – 12 32 = 148 523
© Boardworks Ltd 20136 of 8 Multiplying two matrices List all possible product pairs from the matrices below. Two matrices A and B can be multiplied, but only if the number of columns in matrix A equals the number of rows in matrix B. An m × n matrix can be multiplied by an n × p matrix, and the result is an m × p matrix. 1 4 7 1215 139 127 57 33 129 103 A = B = C = D = Unlike with numbers, the order in which two matrices are multiplied does matter, i.e. AB ≠ BA as a rule.
© Boardworks Ltd 20137 of 8 How to multiply two matrices To multiply two matrices, perform the dot product on rows and columns of the matrices. For larger matrices, start with the first row of the first matrix and perform the dot product on each column of the second. Work through each row of the first matrix in this way. The dot product is the sum of the product of the corresponding entries. For example: 4 5 6 123 = (1 × 4) + (2 × 5) + (3 × 6) = 4 + 10 + 18 = 32
© Boardworks Ltd 20138 of 8 Multiplying two matrices
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Percentage changes © Boardworks Ltd of 22 This icon indicates the slide contains activities created in Flash. These activities are not editable.
Section – Operations with Matrices No Calculator By the end of this lesson you should be able to: Write a matrix and identify its order Determine.
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