Mathematics > QUESTIONS & ANSWERS > ASSESSMENT > MAT 423: ASSESSMENT 2. Q&A (All)

ASSESSMENT > MAT 423: ASSESSMENT 2. Q&A

Document Content and Description Below

MAT 423: ASSESSMENT 2 1. Given the vectors u = (2,1, c), v = (3c, 0, -1) and w = (4, - 2, 0) a. Find the value(s) of the constant c such that u and v are orthogonal. [4 marks] b. Find the angle bet ... ween (2u - v)and w. [6 marks] 30 2. Let W =ax2 + bx + c ,a + b = 2 be a set in P2 a. Give two conditions for W to be a subspace of P2 . [2 marks] b. Determine whether W forms a subspace in P2 . [6 marks] 3. Let M 2 be a set of all follows: 2 with addition and scalar multiplication defined as Where P and Q are vectors in M 22 , and k is a scalar. Determine whether M 2 satisfies the following axiom for any scalar m and n. (m + n)P = mP + nP [5 marks] 4. Let S = (3,2,-5), (0,1,-1), (4,-2,1), (- 3,0,2 a. Determine whether S spans R3 . [5 marks] b. Give reason why S does not form a basis for R3 . [2 marks] [Show More]

Last updated: 2 years ago

Preview 1 out of 4 pages

Buy Now

Instant download

We Accept: