All Questions
19
questions
1
vote
1
answer
48
views
Proof that two matrices are row-equivalent iff they have the same nullspace
The matrices are both of size m x n over some field F, obviously.
The first direction of this proposition is clear enough, however the opposite direction (same nullspace -> row-equivalence) is ...
- 351
2
votes
1
answer
131
views
Do the BEDMAS rules apply to different types of mathematical objects, such as matrices or vectors?
I know that the BEDMAS rules (Brackets - Exponents - Division OR Multiplications - Addition OR Subtraction) for Order of Operations apply to scalars and algebraic expressions.
Do the BEDMAS rules for ...
- 21
3
votes
1
answer
711
views
Matrix-vector multiplication/cross product problem
How can I generally solve equations of the form $\mathbf{A} \mathbf{w} =
\begin{pmatrix} x \\ y \\ z \end{pmatrix}
\times \mathbf{w}$ for the matrix $\mathbf{A},$ where $\mathbf{w}$ can be any vector? ...
- 47
0
votes
2
answers
230
views
Precalculus Vector + Matrix Problem
Every vector $\mathbf{v}$ can be expressed uniquely in the form $\mathbf{a} + \mathbf{b},$ where $\mathbf{a}$ is a scalar multiple of $\begin{pmatrix} 2 \\ -1 \end{pmatrix},$ and $\mathbf{b}$ is a ...
- 47
0
votes
1
answer
64
views
Why Are Some Vector Heads Collinear To Each Other?
The question is as follows:
I thought of the values on the first row and column as x- and y-vector coordinates.
One thing that I do notice in vector M, is that the sum of each of the two columns ...
- 808
-1
votes
1
answer
31
views
Independent vectors multiplied to array help [closed]
Let $\mathbf{A}$ be a matrix, and let $\mathbf{x}$ and $\mathbf{y}$ be linearly independent vectors such that
$\mathbf{A} \mathbf{x} = \mathbf{y}, \mathbf{A} \mathbf{y} = \mathbf{x} + 2\mathbf{y}.$...
- 181
0
votes
1
answer
39
views
Help with Rotational Vector Matrix problem
Let $\mathbf{A}$ be two by two matrix [sqrt(3)/2, -1/2; 1/2, sqrt(3)/2]. Then what is
$\mathbf{A}^{2018} \begin{pmatrix} 2 \\ 2 \end{pmatrix}?$
I am stuck and cannot think of a method of simplifying....
- 181
1
vote
3
answers
2k
views
Show that we can find a matrix $\mathbf{B}$ such that $\mathbf{A} \mathbf{B} = \mathbf{I}$. [closed]
Let $\mathbf{A}$ be a $2 \times 2$ matrix. For every two-dimensional vector $\mathbf{v}$, there exists a two-dimensional vector $\mathbf{w}$ such that
$\mathbf{A} \mathbf{w} = \mathbf{v}.$ Show that ...
- 31
0
votes
2
answers
47
views
Non-bashy Matrix Multiplication
MathStack Exchange professional people,
I had a question about a problem that I was working on for my pre-calculus class.
Here's the problem statement:
The area of the parallelogram with vertices ${...
- 16
1
vote
2
answers
734
views
When getting the cross product of two vectors, is the i value initially positive or negative? [ERROR ON MY END]
[upon further discussion it appears this was just a sign error when performing operations with the matrix (comments in first answer)]
given
$$
\vec{u} = \frac{1}{2} i -1j+\frac{2} {3} k ,\
\...
- 113
0
votes
2
answers
105
views
True or false: For all $A \in \mathbb{R}^{n \times n}$ we get that det($A+A$) $= 2^{n}$ det($A$)
Let $n \in \mathbb{N}$
True or false: For all $A \in \mathbb{R}^{n \times n}$ we get that
det($A+A$) $= 2^{n}$ det($A$)
I did several tests and they all worked fine so I'd say that the ...
- 4,710
0
votes
2
answers
622
views
True or false? The linear system of equations $Ax=b$ is uniquely solvable for every $b \in \mathbb{R}^{n}$ if and only if det(A) $\neq$ 0 [duplicate]
Let $n \in \mathbb{N}$, let $A \in \mathbb{R}^{n \times n}$
True or false? The linear system of equations for $Ax=b$ is uniquely
solvable for every $b \in \mathbb{R}^{n}$ if and only if
$\...
- 4,710
0
votes
1
answer
1k
views
Three vectors are given, choose a basis for the subspace
The subspace $S \subseteq \mathbb{R}^{4}$ is spanned by the vectors
$v_{1}=\begin{pmatrix} 1\\ 2\\ 3\\ 0 \end{pmatrix},
v_{2}=\begin{pmatrix}
-1\\ 5\\ 7\\
-1 \end{pmatrix}, v_{3}=\begin{...
- 4,710
6
votes
3
answers
88
views
Line for set of three-dimensional vectors
If there is a set for 3D vectors $v$ where
$ v \times \begin{pmatrix} -1 \\ 1 \\ 4 \end{pmatrix} = \begin{pmatrix} 5 \\ -27 \\ 8 \end{pmatrix}$
is a line, what is this line's equation?
I'm not sure ...
- 1,725
2
votes
2
answers
314
views
Intersection between two three-dimensional planes
The intersection of the planes defined by
$x \bullet \begin{pmatrix} 8 \\ 1 \\ -12 \end{pmatrix} = 35$
and
$x \bullet \begin{pmatrix} 6 \\ 7 \\ -9 \end{pmatrix} = 70$
is a line. Find an equation of ...
- 1,725