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Kunze Linear Algebra
· Problem 1.3.3
Systems of Linear Equations
Mathematics — Methods · eigenvalue-problems
Problem
If
A
=
[
6
−
4
0
4
−
2
0
−
1
0
3
]
A = \begin{bmatrix} 6 & -4 & 0 \\ 4 & -2 & 0 \\ -1 & 0 & 3 \end{bmatrix}
A
=
6
4
−
1
−
4
−
2
0
0
0
3
find all solutions of
A
X
=
2
X
AX = 2X
A
X
=
2
X
and all solutions of
A
X
=
3
X
AX = 3X
A
X
=
3
X
. (The symbol
c
X
cX
c
X
denotes the matrix each entry of which is
c
c
c
times the corresponding entry of
X
X
X
.)
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