MY-ASSIGNMENTEXPERT™可以为您提供sydney MATH1002 Linear Algebra线性代数的代写代考和辅导服务！
这是悉尼大学线性代数课程的代写成功案例。
MATH1002课程简介
MATH1002 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a foundation requirement in the Faculty of Engineering. This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.
Prerequisites
At the completion of this unit, you should be able to:
- LO1. apply mathematical logic and rigour to solving problems;
- LO2. represent vectors both algebraically and geometrically in two and three dimensions, and perform arithmetic with them;
- LO3. use vectors to solve classical geometric problems;
- LO4. determine spanning families and check linear independence
- LO5. perform and manipulate dot and cross products;
- LO6. set up systems of linear equations;
- LO7. solve systems of linear equations using Gaussian elimination;
- LO8. perform matrix arithmetic and calculate matrix inverses and determinants;
- LO9. find eigenvalues and eigenvectors;
- LO10. diagonalise a matrix;
- LO11. express mathematical ideas and arguments coherently in written form.
MATH1002 Linear algebra HELP（EXAM HELP， ONLINE TUTOR）
Which of the following equations are linear equations in $x, y$ and $z$ ? If they are not linear explain why not.
(a) $x-y-z=3$
(b) $\sqrt{x}+y+z=6$
(c) $\cos (x)+\sin (y)=1$
(d) $e^{x+y+z}=1$
(e) $x-2 y+5 z=\sqrt{3}$
(f) $x=-3 y$
(g) $x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$
(h) $\pi x+y+e z=5$
(i) $\sqrt{2} x+\frac{1}{2} y+z=0$
(j) $\sinh ^{-1}(x)=\ln \left|x+\sqrt{x^2+1}\right|$
(k) $\frac{\pi}{2} x-\sqrt{2} y+z \sin (\pi)=0$
(l) $x^{2^0}+y^{3^0}+z^{3^0}=0$
(m) $y^{\cos ^2(x)+\sin ^2(x)}+x-z=9$
(a) Linear
(e) Linear
(i) Linear
(m) Linear
(b) Not linear
(f) Linear
(j) Not linear
(c) Not linear
(g) Linear
(k) Linear
(d) Not linear
(h) Linear
(l) Linear
Solve the following linear system by the elimination process discussed in this section.
(a)
[Y][Y]=[V]
(b)
$$
2 x-3 y=5
$$
$x-y=0$
$x-y=2$
(c)
$$
2 x-3 y=35
$$
$$
x-y=2
$$
(d)
(e)
$$
\pi x-5 y=2
$$
(f)
$$
e x-e y=2
$$
$9 x-3 y=6$
$$
\pi x-y=1
$$
$$
e x+e y=0
$$
(In part (f), $e$ is the irrational number $e=2.71828182846 \cdots$ )
(a) $x=1, y=1$
(b) $x=1, y=-1$
(c) $x=-29, y=-31$
(d) $x=\frac{3}{4}, y=\frac{1}{4}$
(e) $x=\frac{3}{4 \pi}, y=-\frac{1}{4}$
(f) $x=\frac{1}{e}, y=-\frac{1}{e}$
Solve the following linear systems by the elimination process discussed in this section.
$$
x+y+z=3
$$
$$
x+2 y-2 z=6
$$
(a)
$$
\begin{aligned}
x-y-z & =-1 \
2 x+y+5 z & =8 \
3 x+y-2 z & =4
\end{aligned}
$$
(b)
$$
\begin{aligned}
& 2 x-3 y+z=-10 \
& 3 x-y+3 z=-16 \
& 6 x-3 y+2 z=31
\end{aligned}
$$
$$
6 x-3 y+2 z=31
$$
(c)
$$
\begin{aligned}
& 5 x-3 y+10 z=32 \
& 7 x+4 y+16 z=13
\end{aligned}
$$
(d)
$$
\begin{aligned}
5 x+y+12 z & =36 \
8 x+5 y+z & =11
\end{aligned}
$$
(a) $x=y=z=1$
(b) $x=-2, y=1$ and $z=-3$
(c) $x=3, y=-4$ and $z=\frac{1}{2}$
(d) $x=3, y=-3$ and $z=2$
Plot the graphs of these linear equations and decide on the number of solutions of each linear system. If there are any solutions, find them.
(a)
$2 x+y=3$
(b)
$2 x+y=3$
$x-y=7$
$8 x+4 y=12$
(c)
$2 x+y=3$
$2 x+y=5$
(d)
$3 x-2 y=3$
(e) $3 x-2 y-3=0$
$3 x-2 y=6$
(e) $3 x-2 y-5=0$
(f)
$5 x-2 y-5=0$
$3 x-2 y-3=0$
(a) Unique
(b) Infinite
(c) No solution
(d) No solution
(e) No solution
(f) Unique
MY-ASSIGNMENTEXPERT™可以为您提供SYDNEY MATH1002 LINEAR ALGEBRA线性代数的代写代考和辅导服务！
