Question: Question 4 Consider the line 3; = 3:1: in the plane. The aim of this question is to nd the 2 x 2 matrix A

Question 4 Consider the line 3; = 3:1: in the plane. The aim of this question is to nd the 2 x 2 matrix A that orthogonally projects a vector to this line. (a) Find 8. equation of the line, in the form y = ma: + b, that is perpendicular to the line y = 3a: and passes through the point P = (p1, p2). (b) Using part (a) show that the vector (7% is projected to 14(03): ($101 + $02) ' 13-0121 + 1901 (c) Use the result of (b) to write the matrix A. (d) Write down two different, non-zero vectors Ff and 32) such that A171 = A si

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