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Homework 1 MAT 281E

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Number: Homework 1
MAT 281E

1. (40 pts.)For each of the following express the linear system in matrix form.
i)
x + y + 3z = 8
− x + 2y + 3z = 1
3x − 7y + 4z = 10
ii)
2x + 2y + 2z = 0
− 2x + 5y + 2z = 1
8x + y + 4z = −1
a) Solve the linear system (if any) by Gaussian Elimination
b) Solve the linear system (if any) by Gauss-Jordan Elimination
2
Name:
Number: Homework 1
MAT 281E
October 9, 2019
2. (30 pts.) If
M =


2 −1
3 6
−2 5

 and N =

1 7
3 −6

verify that
a) 3(MN) = (3M)N = M(3N)
b) (MN)
T = NTMT
3
Name:
Number: Homework 1
MAT 281E
October 9, 2019
3. (30 pts.) Let A3 − 5A2 + 7A = 0
Write down a formula for A−1
in terms of A and I.
4

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