STA4803 Assignment 1 (185549)|COMPLETE SOLUTIONS| - DUE 28 MAY 2026

STA4803
Assignment 1
(185549)

DUE: 28 MAY 2026

, ASSIGNMENT 01

Unique Number: 185549.

Closing Date: 28 May 2026.




QUESTION 1 [27 Marks]

1.1 Row Echelon Form of Matrix B

First, we define 𝐵 from the given 𝑡𝐵. Since 𝑡𝐵 is 3 × 4, 𝐵 is a 4 × 3 matrix:

5 4 1
8 6 1
𝐵= 1
2 7
4
[4 0 2]

Elementary Row Operations:

1 0.8 0.2
1 8 6 1
1. 𝑅1 → 𝑅1 : [ ]
5 2 7 0.25
4 0 2
1 0.8 0.2
0 −0.4 −0.6
2. 𝑅2 → 𝑅 2 − 8𝑅1 , 𝑅3 → 𝑅 3 − 2𝑅1 , 𝑅4 → 𝑅 4 − 4𝑅1 : [ ]
0 5.4 −0.15
0 −3.2 1.2
1 0.8 0.2
0 1 1.5
3. 𝑅2 → −2.5𝑅 2 : [ ]
0 5.4 −0.15
0 −3.2 1.2
1 0.8 0.2
0 1 1.5
4. 𝑅3 → 𝑅 3 − 5.4𝑅2 , 𝑅4 → 𝑅 4 + 3.2𝑅2 : [ ]
0 0 −8.25
0 0 6
1 0.8 0.2
1 0 1 1.5
5. 𝑅3 → − 𝑅 :[ ]
8.25 3 0 0 1
0 0 6