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Problems
Let
A
=
(
4
−
1
2
3
)
and
Y
(
t
)
=
(
2
t
+
1
t
−
3
)
,
A=\begin{pmatrix}4 & -1\\ 2 & 3\end{pmatrix}\quad\text{and}\quad Y(t)=\begin{pmatrix}2t+1\\ t-3\end{pmatrix},
A
=
(
4
2
−
1
3
)
and
Y
(
t
)
=
(
2
t
+
1
t
−
3
)
,
…
Mathematics
Problem
Let
A
=
(
4
−
1
2
3
)
and
Y
(
t
)
=
(
2
t
+
1
t
−
3
)
,
A=\begin{pmatrix}4 & -1\\ 2 & 3\end{pmatrix}\quad\text{and}\quad Y(t)=\begin{pmatrix}2t+1\\ t-3\end{pmatrix},
A
=
(
4
2
−
1
3
)
and
Y
(
t
)
=
(
2
t
+
1
t
−
3
)
,
where
t
t
t
is a real parameter. a. (i) Obtain the general solution vector
X
(
t
)
=
(
x
(
t
)
y
(
t
)
)
X(t)=\begin{pmatrix}x(t)\\y(t)\end{pmatrix}
X
(
t
)
=
(
x
(
t
)
y
(
t
)
)
of the system
A
X
=
Y
(
t
)
AX=Y(t)
A
X
=
Y
(
t
)
. b. (ii) Using the result from part (i), find the numerical values of
x
x
x
and
y
y
y
when
t
=
2
t=2
t
=
2
.
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