Question: Question 3 (10 marks) a} Given that set B = {(1,2,1),(1,1,2),{1,1,3}} is a basis of R3. 1. What is the transition matrix which will change

Question 3 (10 marks) a} Given that set B = {(1,2,1),(1,1,2),{1,1,3}} is a basis of R3. 1. What is the transition matrix which will change bases from B to the standard basis of R3? (1 mark) ii. What is the transition matrix that will change bases from the standard basis of R3 to B. [3 marks) 13} A transformation f : 1R3 } R3 is dened by f(3113321$3)= (1:1 2332 + 33,431 + 332 + 25.33, 2331 + 332 + 333}. 1. Show that f is a linear transformation. [2 marks) ii. Write down the standard matrix of f, i.e. the matrix with respect to the standard basis of IF. [2 marks) iii. Show that f is a onetoone transformation. [2 marks)

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