Mathematics > QUESTIONS & ANSWERS > ASSESSMENT > Sept19_Assessment 3_SOLNS _ FACULTY OF COMPUTER AND MATHEMATICAL SCIENCES MAT 423 LINEA (All)

ASSESSMENT > Sept19_Assessment 3_SOLNS _ FACULTY OF COMPUTER AND MATHEMATICAL SCIENCES MAT 423 LINEAR ALGEBRA ASSESSMENT 3

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FACULTY OF COMPUTER AND MATHEMATICAL SCIENCES MAT 423 LINEAR ALGEBRA ASSESSMENT 3 [SEPT 2019 – JAN 2020] Answer ALL questions. Duration: 1 hr 15 mins QUESTION 1 a) Find the vector v which has ... a magnitude of 14 units and is in the opposite direction to u = (2 , 5 , -4 , -2) . (3 marks) b) Given the vectors r = (3 , 0 , 2) , s = (-1 , 4 , -2) , and t = (0 , -2 , k + 3) , find: i) w = 2 r + s . ii) The constant k such that t is orthogonal to w . iii) The angle θ between r and s . (7 marks QUESTION 2 a) Suppose V is a set of vectors in R3 with addition and scalar multiplication defined as follows: (u1 , u2 , u3) + (v1 , v2 , v3) = (u1 , v2 , u3 - v3) , k (u1 , u2 , u3) = (k u1 , k , k u3) , where k is any scalar. Determine whether k (u + v) = k u + k v for any u and v in V . (5 marks) b) Consider the set Q = {a0 + a1 x + a2 x2 , where a2 = 2 (a1 + a0)} . Determine whether Q is a subspace of P2 where P2 is the set of real polynomials of degree less than or equal to 2. (8 marks) QUESTION 3 Consider the set S = {[1 0 1 1], [-11 0 1], [2 0 1 1], [0 2 0 2]} . a) State the two conditions for S to be a basis for M2x2 . b) Determine whether the set S is a basis for M2x2 . (7 marks) [Show More]

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