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MAT3701 Assignment 4 Solutions 2026

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MAT3701 Assignment 4 Solutions 2026 unisa due: 15 july 2026

Institution
University Of South Africa (Unisa)
Course
Linear Algebra III (MAT3701)

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MAT3701 Assignment 4 Solutions 2026
UNISA
DUE: 15 JULY 2026

, Question 1

Given
1 1
𝐴=( )
1 1


Question 1.1

Verify that
1
𝑣1 = ( )
−1


is an eigenvector and determine its eigenvalue.

Calculate
1 1 1
𝐴𝑣1 = ( )( )
1 1 −1


First row:

1(1) + 1(−1) = 0


Second row:

1(1) + 1(−1) = 0


Hence
0
𝐴𝑣1 = ( )
0


Since
1 0
0 ( ) = ( ),
−1 0


we obtain

𝐴𝑣1 = 0𝑣1 .


Therefore
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