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5.3d Describing the Combination of Two Transformations Given the Object and the Image Example 1: In the diagram above, triangle KLM is the image of triangle ABC under the combined transformations VW. Describe in full, the transformation W and the transformation V. Solution: Figure ABC → W→ Figure KB’C’ → V → Figure KLM W = … Read more
5.3c Stating the Coordinates of the Image of a Point under a Combined Transformation 1. The coordinates of the image of a point, K, under the combined transformation AB can be determined by the following steps. Step 1: Determine the coordinates of K’, the image of K, under the first transformation, B. Step 2: … Read more
5.3b Determining the Image of an Object under Combination of (a) Two Enlargements or (b) an Enlargement and an Isometric Transformation 1. Enlargement is a transformation where all points of an object on a plane move from a fixed point at a constant ratio. 2. The fixed point is called the centre of enlargement and … Read more
5.3a Determining the image of an object under the combination of two isometric transformations 1. Translations, reflections and rotations are isometric transformations. 2. In an isometric transformation, the shape and the size of the image is the same as the object. 3. For two transformations, A and B, (a) Combined transformation AB represents transformation B followed … Read more
Question 10:It is given that matrix M is a 2 × 2 matrix such that M( −2 1 1 3 )=( 1 0 0 1 ) (a) Find matrix M. (b) Write the following simultaneous linear equations as matrix equations: –2x + y = 10 x + 3y = 9 Hence, using matrix method, calculate the value of x and of … Read more
Question 1: It is given that matrix A = ( 3 − 1 5 − 2 ) (a) Find the inverse matrix of A. (b) Write the following simultaneous linear equations as matrix equation: 3u – v = 9 5u – 2v = 13 Hence, using matrix method, calculate the value of u and v. … Read more
2.9.2 Matrices, SPM Practice (Short Questions) Question 5: Given that ( 3 x ) ( x − 1 ) = ( 18 ) , find the value of x. Solution: ( 3 x ) ( x − 1 ) = ( 18 ) [3 × x + x (–1)] = (18) 3x – … Read more
Question 1: ( 1 4 6 2 ) + 3 ( 2 0 4 − 3 ) − ( − 3 0 − 2 − 5 ) Solution: ( 1 4 6 2 ) + 3 ( 2 0 4 − 3 ) − ( − 3 0 − 2 − 5 ) = ( … Read more
2.8 Solving Simultaneous Linear Equations using Matrices 1. Two simultaneous linear equations can be written in the matrix equation form. For example, in the simultaneous equations: ax + by = e cx + dy = f can be written in the matrix form as follows: ( a b c d ) ( x y ) = ( e … Read more
2.7 Inverse Matrix 1. If A is a square matrix, B is another square matrix and A × B = B × A = I, then matrix A is the inverse matrix of matrix B and vice versa. Matrix A is called the inverse matrix of B for multiplication and vice versa. 2. The symbol A-1 denotes the inverse matrix … Read more