Grade 9 Mathematics Paper 1 - 2019, Question 11. a) State the order of matrix P, b) find 2P Solutions Q11. (a) The order of a matrix is determined by the number of rows and columns it has. It can be defined by the number of rows times the number of columns (number of rows x number of columns.) A matrix with m rows and n columns would be called an m by n matrix ( m x n matrix.) Therefore, in order for us to know the order of the matrix P, we will count the number of rows and columns and then join them together in the form of m x n. Step 1; Count the number of rows. ( remember, rows run horizontally) If we count the number of lines running through the matrix horizontally, we get 2. Therefore there are 2 rows. If we count the number of lines running through the matrix vertically, we get 3. Therefore there are 3 columns. = 2 rows x 3 columns = 2 x 3 therefore, The order of matrix P is; 2 x 3 Q11. (b) In order for us to find 2P, we multiply each element in the matrix by 2 as follows Another way to solve this problem is by dealing with it in terms of addition. Remember that multiplication is just repeated Addition, e.g. 2 x 3 = 2 + 2 + 2 (When we say 2 x 3, we are saying repeat 2 three times using = 3 + 3 operation of addition or repeat 3 two times by the operation of addition) 2 x 7 = 2 + 2 + 2 + 2 + 2 + 2 + 2 (When we say 2 x 7, we are saying repeat 2 seven = 7 + 7 times by the operation of addition or repeat 7 two times by the operation of addition Therefore when we say 2P(2 x P), we are saying repeat P two times using the operation of addition as shown below. 2P = P + P We can now evaluate P + P to get the answer. When adding matrices, you add the corresponding terms. For example, given the matrices below, the first term of A will be added to the first term of B, the second term of A will be added to the second term of B and so on. Therefore we can add P + P in the same manner as follows; Help support this work, to ensure the continued growth of this platform, any amount will be greatly appreciated. You can also donate school material.
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