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What is a matrix?

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.

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What is a matrix?

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  1. 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. Saturday Sunday 129 105 Men 129 105 103 99 Women 103 99 80 67 Children 80 67 This is a 3 × 2 (“3 by 2”) matrix because it has 3 rows and 2 columns. It contains 6 elements or entries.

  2. Adding matrices Two matrices can be added or subtracted if they have the same dimensions. Add each corresponding element from both matrices to get the resulting element. 6 + 12 5 + 4 6 5 12 4 –2 + 1 13 – 3 –2 13 1 –3 For example: + = 8 + 2 –17 + 0 8 –17 2 0 18 9 –1 10 = 10 –17

  3. Adding and subtracting matrices

  4. 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. 7 5 7 × 3 5 × 3 21 15 3 2 3 × 3 2 × 3 9 6 For example: 3 = = 11 1 11 × 3 1 × 3 33 3 Calculate: 1 2 3 2 5 – 3 2 11 1 1 2 14 8 15 10 = = – 3 2 52 3 55 5

  5. Multiplying two matrices 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. Unlike with numbers, the order in which two matrices are multiplied does matter, i.e. AB ≠ BA as a rule. List all possible product pairs from the matrices below. 12 7 1 129 12 15 C = D = A = B = 5 7 4 103 13 9 3 3 7

  6. How to multiply two matrices To multiply two matrices, perform the dot product on rows and columns of the matrices. The dot product is the sum of the product of the corresponding entries. = 1 2 3 For example: 4 (1 × 4) + (2 × 5) + (3 × 6) 5 6 32 = = 4 + 10 + 18 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.

  7. Multiplying two matrices

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