UNISA
Assignment 4
MAT1503
, Question 1
1.1)
2 −1 1
A = [3 1 −1],
1
1 −3 𝑘 4
E1 = row operation R2 – 2R1 → R2 to A
1 0 0 1 0 0
𝐸 = [0 1 0 ] then E 1 = [−2 1 0]
0 0 1 0 0 1
E1A = B
1 0 0 2 −1 1
[−2 1 0] [3 1 −1
1
]=B
0 0 1 1 −3 𝑘 4
2 −1 1
B = [−1 3 −3]
1
1 −3 𝑘 4
1
a33 = 𝑘 4
a33 = 𝑎33 2
1 1
𝑘 4 = (𝑘 4 )2
1 1
𝑘4 = 𝑘2
k = k2
k – k2 = 0
k (1 – k) = 0
Therefore k = 0 and k = 1.
Assignment 4
MAT1503
, Question 1
1.1)
2 −1 1
A = [3 1 −1],
1
1 −3 𝑘 4
E1 = row operation R2 – 2R1 → R2 to A
1 0 0 1 0 0
𝐸 = [0 1 0 ] then E 1 = [−2 1 0]
0 0 1 0 0 1
E1A = B
1 0 0 2 −1 1
[−2 1 0] [3 1 −1
1
]=B
0 0 1 1 −3 𝑘 4
2 −1 1
B = [−1 3 −3]
1
1 −3 𝑘 4
1
a33 = 𝑘 4
a33 = 𝑎33 2
1 1
𝑘 4 = (𝑘 4 )2
1 1
𝑘4 = 𝑘2
k = k2
k – k2 = 0
k (1 – k) = 0
Therefore k = 0 and k = 1.
