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Mathematics
Mathematics
Problem
Consider the matrix
B
(
t
)
=
(
t
+
2
3
4
t
−
1
)
,
B(t)=\begin{pmatrix}t+2 & 3\\4 & t-1\end{pmatrix},
B
(
t
)
=
(
t
+
2
4
3
t
−
1
)
,
where
t
∈
Z
t\in\mathbb Z
t
∈
Z
. a. (i) Obtain
det
(
B
(
t
)
)
\det\bigl(B(t)\bigr)
det
(
B
(
t
)
)
as a polynomial in
t
t
t
. b. (ii) Find all integers
t
t
t
with
−
5
≤
t
≤
5
-5\le t\le5
−
5
≤
t
≤
5
for which
B
(
t
)
B(t)
B
(
t
)
is invertible.
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