Mat1511 Assignment 4 2025

MAT1511
ASSIGNMENT 4 2025
DUE: JULY 2025 (MEMO)

, MAT1511 Assessment 4
Question 1


⎧−x + 2y + 3z = 11,
⎨ 2x − 3y = −6,
​ ​




⎩
3x − 3y + 3z = 3.

Form the augmented matrix and use row operations. For clarity, multiply the first equation
by –1 to start with a leading 1:

1 −2 −3 ∣ −11
2 −3 0 ∣
​ ​ ​ ​ ​ −6 . ​ ​




3 −3 3 ∣ 3

Eliminate x from the other rows:

R2 ← R2 − 2R1 :
​ ​ ​




R2 : [2 − 2 ⋅ 1 = 0, −3 − 2(−2) = 1, 0 − 2(−3) = 6, −6 − 2(−11) = 16].
​




R3 ← R3 − 3R1 :
​ ​ ​




R3 : [3 − 3 = 0, −3 − 3(−2) = 3, 3 − 3(−3) = 12, 3 − 3(−11) = 36].
​




Now the matrix is

1 −2 −3 ∣ −11
0 1
​ 6 ∣​ ​ ​ ​ 16 . ​ ​




0 3 12 ∣ 36

Next eliminate y from row 3: R3← R3 − 3R2 :
​ ​ ​




R3 : [0, 3 − 3(1) = 0, 12 − 3(6) = −6, 36 − 3(16) = −12]. Divide R3 by −6:
​ ​




R3 : [0, 0, 1, 2].
​




The matrix is now in row-echelon form:

1 −2 −3 ∣ −11
0 1
​ 6 ∣​ ​ ​ ​ 16 . ​ ​




0 0 1 ∣ 2

Back-substitute:

From R3 : z
​ = 2.