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MEI FP1 Study Resources Further Pure Matrices 1-4 by Catherine Berry

By Catherine Berry

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Extra info for MEI FP1 Study Resources Further Pure Matrices 1-4

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You may also be asked to use it for three equations in three unknowns, but in that case you would always be given help in finding the inverse matrix. Questions 5 – 7 in Exercise 2G are of this type. There is a PowerPoint presentation which shows examples involving 3 × 3 matrices. You may find this helpful when you are attempting questions 5 – 7 in Exercise 2G. It is very important that you understand the three possible situations with two equations in two unknowns, and their geometrical interpretations.

Calculate the angle of rotation and the scale factor of the enlargement. © MEI, 14/12/06 2/2 Further Pure Mathematics 1 Matrices Section 2: Matrix multiplication Solutions to Exercise ⎛ 0 1 0 −1 ⎞ 1. (i) S = ⎜ ⎟ ⎝0 1 2 1 ⎠ 6 −1 ⎞ ⎛ 4 3 ⎞ ⎛ 0 1 0 −1 ⎞ ⎛ 0 7 = (ii) ⎜ −3 −2 ⎟ ⎜ 0 1 2 1 ⎟ ⎜ 0 −5 −4 1 ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠ The image of the square has vertices at (0, 0), (7, -5), (6, -4) and (-1, 1). (iii) ⎛ 3 0 ⎞⎛0 1 1 0⎞ ⎛0 3 3 0 ⎞ 2. ⎜ ⎟⎜ ⎟=⎜ ⎟ ⎝ 0 2 ⎠⎝0 0 1 1 ⎠ ⎝0 0 2 2 ⎠ The transformation is a two-way stretch, with scale factor 3 parallel to the xaxis, and scale factor 2 parallel to the y-axis.

There are some additional notes in the Notes and Examples. 2. For practice in this work, try the interactive questions Find the inverse of a 2 by 2 matrix. 3. Exercise 1E Attempt all the questions. The syllabus only requires you to be able to find the inverse of a 2 × 2 matrix, but notice that Question 6 involves 3 × 3 matrices. Here you are given help in finding the inverses. This type of question does sometimes come up in exams, but you will not be expected to find the inverse of a 3 × 3 matrix without guidance.