Recent content by shamieh

Find a set of vectors {u, v} in $\mathbb{R}^4$ that spans the solution set of the equations: $x - y + 2z - 2w = 0$ $2x + 2y -z + 3w = 0$ ($u$ and $v$ are both $4 \times 1$) $u = ?$, $v = ?$ I put the matrix in RREF to get $\begin{bmatrix}1&0&3/4&-1/4\\0&1&-5/4&7/4\end{bmatrix} =...

Let the matrix $M = \begin{bmatrix}-12&-12&16&-15\\-6&-8&-8&-10\\0&20&0&25\end{bmatrix}$ Find a non zero vector in the column space of $M$ Is it not true that $\begin{bmatrix}-12\\-8\\20\end{bmatrix}$ is a non zero vector in the column space of $M$ ? For some reason it keeps telling me "that...

How can I find out if this matrix A's columns are linearly independent? $\begin{bmatrix}1&0\\0&0\end{bmatrix}$ I see here that $x_1 = 0$ and similarly $x_2 = 0$ does this mean that this matrix A's columns are therefore linearly dependent? Also this is a projection onto the $x_1$ axis so is it...

a) $f_1 = O(f_2)$ b) $f_1 = O(f_2)$ c) According to the definition I know that: $f(x)=O(g(x))$ iff $∃$ positive constants $C$ and $n_0 |0≤f(n)≤c∗g(n), ∀ n≥n_0|$ So letting $n = 10$, $c = 5$ for: $0 \le f_1(n) \le c * f_2(n) \implies (10)^2 + (10)\log(10) \le (5)((10)\log^4 (10) +...

Wow thanks so much.. So now I'm on the second part.. (NOTE: I left out $h$ for the time being) But I'm not sure if I'm doing it right. Here is what I have so far: a) $f_1 = O(f_2)$ b) Not Equal c) Not Equal Justification: $n^2 = 1000^2 =$ 1 million while $(1000)\log^4 (1000) = 2.27..$ so we...

Here is what I've came up with.. I know that: $f(x) = O(g(x))$ iff $\exists$ positive constants $C$ and $n_0$ $|0 \le f(n) \le c * g(n),$ $\forall$ $n \ge n_0|$ So I found that $n! \notin O(4^n)$ by letting $n = 10$ and letting $c = 1$. Then I found that $4^n \in O(4^n)$ is that the correct...

Which of the following identities are true. Justify your answer. a)$n! = O(4^n)$ b)$4^n = O(n!)$ I have NO clue what to do here. First I was thinking let $n = 0$ so that $1 = O(1)$ (constant time complexity?)

Can someone tell me if I'm even doing this correctly? I haven't dealt with TCs in while. So I got: $a) h_1(n) = O(n) \implies n$ , $h_2(n) = \Omega (n\log n) \implies n\log n$ $b) h_1(n) = \Omega(\log n) \implies \log n$, $h_2(n) = O(n^{2/5}) \implies n^{2/5}$ (Justification $h_1(n)$: Let $n...

|Ok I think I've figured it out.. Can someone check my work? Sorry to be a pest with the triple posts... $A = \{w,x,y,z\}$ $U = \{w,y\} * A^7$ $S = \{w,y\} * \{w,y,z\}^7$ $|U - S| = |U| - |S|$ $= |\{w,y\} * A^7| - |\{w,y\} * \{w,y,z\}^7|$ $= |\{w,y\}||A|^7 - |\{w,y\}||\{w,y,z\}|^7$ $=...

Wait.. am I making this harder than it is? Is that just $4^8$

Count the number of strings of length $8$ over $A = \{w, x, y, z\}$ that begins with either $w$ or $y$ and have at least one $x$ I don't understand this question at all. First of all, this is a set A that contains 4 elements $w,x,y,z$ correct? They are asking me to count the number of strings...

Ahh, nevermind, re-working

Use the component method to add the vectors A and B shown in the figure. Both vectors have magnitudes of 3.55 m and vector A makes an angle of $θ = 28.5°$ with the x axis. Express the resultant A + B in unit-vector notation. I don't understand how my answer is wrong. Isn't it $A + B =...

Object: Black Plastic Lid $C$ = Circumference (cm) $D$ = Diameter (cm) Ratio $= \frac{C}{D}$ Ratio $= \frac{30.75}{9.46} = 3.25$

UPDATE! The correct solutions for part b) and part c) are: b) $a_0 = 1$ $a_1 = 0$ $a_2 = -2/3$ $a_3 = 0$ $a_4 = 0$ $\therefore$ $y_1 = 1 + (-\frac{2}{3}x^2) + ... + ...$ c) $a_0 = 0$ $a_1 = 1$ $a_2 = 0$ $a_3 = -2/3$ $a_4 = 0$ $a_5 = 1/15$ $\therefore$ $y_2 = x + (-\frac{2}{3}x^2) +...