3D CAD Modeling Answers

Based on the circuit, program and the given conditions,
(a) Complete the circuit. For the microcontroller, show only the port and pins connected to the DAC. The connections of the DAC0808 and the Op-Amp must be shown in details.

(b) Sketch and label the output waveform of this circuit for 2 cycles. Show the necessary calculations.

(c) Rewrite the given program in C language. Show only the main function. Use the library function Delay10TCY(x) to generate the desired delay.

a) Let V =
{
(a; b; c; d ) 2 R
4
ja + b + 2c + 2d = 0
}
and
W =
{
(a; b; c; d ) 2 R
4
ja = b; c = d
}
. Check that V and W are vector spaces.
Further, check that W is a subspace of V . (4)
b) Find the dimensions of V and W . (3)
c) Let P
3
=
{
ax
3
+ bx
2
+ cx + d ja; b; c; d 2 R
}
. Check whether f (x) = x
2
+ 2x + 1 is in
[S], the subspace of P
3
generated by S =
{
3x
2
+ 1; 2x
2
+ x + 1
}
. If f (x) is in [S], write
f as a linear combination of elements in S. If f (x) is not in [S], find another
polynomial g(x) of degree at most two such that f (x) is in the span of S [ fg(x)g. Also
write f as a linear combination of elements in S [ fg(x)g.