. (a) Vectors in R are defined by a = (3,-1, 12) and b = (4,2,3)....

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. (a) Vectors in R are defined by a = (3,-1, 12) and b = (4,2,3). (i) Determine 4a - 6b. (ii) Calculate a. b. (iii) Find the length of the vector 3a - b. (iv) Determine a x (a x b). (b) Show that the following set of vectors form a basis for R B= 2 -{0) (0) (\)} 5 (c) Determine the change of basis matrix AB such that AE+B[U]E = [u]B, where E ={i, j, k} is the standard basis. Uses your matrix to ex- press the vector [(2,2,1)] E with respect to the basis B from part (b). [2] [2] [3] [4] [5] [9] . (a) Vectors in R are defined by a = (3,-1, 12) and b = (4,2,3). (i) Determine 4a - 6b. (ii) Calculate a. b. (iii) Find the length of the vector 3a - b. (iv) Determine a x (a x b). (b) Show that the following set of vectors form a basis for R B= 2 -{0) (0) (\)} 5 (c) Determine the change of basis matrix AB such that AE+B[U]E = [u]B, where E ={i, j, k} is the standard basis. Uses your matrix to ex- press the vector [(2,2,1)] E with respect to the basis B from part (b). [2] [2] [3] [4] [5] [9]

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a Given vectors a 3 1 12 and b 4 2 3 i 4a 6b 43 1 12 64 2 3 12 4 48 24 12 18 36 8 66 ii ab 34 12 123 12 2 36 46 iii 3a b 9 3 36 4 2 3 5 5 33 sqrt52 52 ... View the full answer