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Question 1 Continued A=2 c) Given the following column vectors: - (1 ) and . = (b) B=8 C=5 i) Are these vectors linearly independent? Justify your answer. (3 marks) i) Plot vectors u and v. (2 marks) iii) Are the vectors u and 17 orthogonal? Justify your answer. (3 marks) d) Investigate whether the following column vectors form a basis for IR". (Use the reduced row echelon form method). V1 12 V3 VA O (12 marks) e) Hence, show that vector 14 can be written as a linear combination of the vectors V1, V2 and Va- (2 marks) f) Briefly describe what the result in part e) might mean in practical terms. (2 marks) g) Obtain the eigenvalues and eigenvectors for the matrix S given below. Hence, use your results to explain in context why diagonalization of a matrix might be useful. - 12 -10