Mathematics > QUESTIONS & ANSWERS > MAT 423 LINEAR ALGEBRA ASSESSMENT 3 - ALL ANSWERS ARE CORRECT (All)

MAT 423 LINEAR ALGEBRA ASSESSMENT 3 - ALL ANSWERS ARE CORRECT

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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) SOLUTION a )Method 1 G iven that v → is a vector of magnitude 14 that is in the opposite direction as u → . ∴ The unit vector for v → is in the opposite direction as the unit vector for u → . ⇒ v → ‖v → ‖ = − u → ‖u → ‖ ⇔ v → 14 = − (2 , 5 , −4 , −2) √2 2 + 5 2 + (−4 ) 2 + (−2) 2 ⇔ w → = − 14 (2 , 5 , [Show More]

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