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Problem
Problem
Let matrix
A
=
[
x
3
2
1
y
4
2
2
z
]
A = \begin{bmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{bmatrix}
A
=
x
1
2
3
y
2
2
4
z
; if
x
y
z
=
2
λ
xyz = 2\lambda
x
y
z
=
2
λ
and
8
x
+
4
y
+
3
z
=
λ
+
28
8x + 4y + 3z = \lambda + 28
8
x
+
4
y
+
3
z
=
λ
+
28
, then
(
adj
A
)
A
(\text{adj } A) A
(
adj
A
)
A
equals : (a)
[
λ
+
1
0
0
0
λ
+
1
0
0
0
λ
+
1
]
\begin{bmatrix} \lambda + 1 & 0 & 0 \\ 0 & \lambda + 1 & 0 \\ 0 & 0 & \lambda + 1 \end{bmatrix}
λ
+
1
0
0
0
λ
+
1
0
0
0
λ
+
1
(b)
[
λ
0
0
0
λ
0
0
0
λ
]
\begin{bmatrix} \lambda & 0 & 0 \\ 0 & \lambda & 0 \\ 0 & 0 & \lambda \end{bmatrix}
λ
0
0
0
λ
0
0
0
λ
(c)
[
λ
2
0
0
0
λ
2
0
0
0
λ
2
]
\begin{bmatrix} \lambda^2 & 0 & 0 \\ 0 & \lambda^2 & 0 \\ 0 & 0 & \lambda^2 \end{bmatrix}
λ
2
0
0
0
λ
2
0
0
0
λ
2
(d)
[
λ
+
2
0
0
0
λ
+
2
0
0
0
λ
+
2
]
\begin{bmatrix} \lambda + 2 & 0 & 0 \\ 0 & \lambda + 2 & 0 \\ 0 & 0 & \lambda + 2 \end{bmatrix}
λ
+
2
0
0
0
λ
+
2
0
0
0
λ
+
2
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