MAT2611 Assignment 4 2025 - Die 30 May 2025

MAT2611
ASSIGNMENT 4
DUE: 30 MAY 2025

, MAT2611
ASSIGNMENT 04
Due date: Friday, 30 May 2025




Problem 1. Find the coordinate=vectors 2 =
(3; 2; of(; vv2;
1) relative
1; 0) ; vto
3 =
the
(5;basis
0; 0).of set
1
S = fv1 ; v2 ; v3 g; where v = (3; 4; 3); v




Problem 1


Coordinate vector of v relative to basis S :
To find [v]S ​ = (a, b, c), solve:

3a − 2b + 5c = 3, 2a + b = 4, a = 3.

3 Substitute :




2(3) + b = 4 ⟹ b = −2, 3(3) − 2(−2) + 5c = 3 ⟹ c = −2.



Coordinate vector:



[3, −2, −2] ​




x3 = 0
​