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...
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...
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...
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 =...