Linked Questions

0
votes
1answer
107 views

How to find the intersection of $W$ and $Z$? [duplicate]

Subspaces$W$ and $Z$ of $\mathbb R^4$ are generated by $\{(1,1,0,-1),(1,2,3,0),(2,3,3,-1)\}$ and $\{(1,1,0,-1),(1,2,3,4),(0,1,3,5)\}$, respesctively. Find a basis for $W$$\cap$$Z$. I already ...
0
votes
1answer
49 views

Find Basis of $\mathrm{Col}(A) \cap \mathrm{Row}(A)$ [duplicate]

Let $$A= \begin{pmatrix}1&-4&-1&2\\ 1&-4&1&2\\ 4&-16&-7&7\\ -1&4&8&-1\end{pmatrix} $$ Find Basis of $\mathrm{Col}(A) \cap \mathrm{Row}(A)$ I found ...
7
votes
2answers
13k views

Calculating dimension of the intersection of two subspaces

Q. Let $U$ be the vector subspace of $\Bbb R^5$ generated by $\{(1,3,-3,-1,-4),(1,4,-1,-2,-2),(2,9,0,-5,-2)\}$, and let $V$ be the vector subspace of $\Bbb R^5$ generated by $\{(1,6,2,-2,3),(2,8,-1,-6,...
3
votes
1answer
2k views

Finding a basis for intersection of two subspaces

Let two subspaces of $V=\mathbb{R}^4$: $$w1 = \left\{ {\left( {\matrix{ 1 \cr 1 \cr 1 \cr 1 \cr } } \right),\left( {\matrix{ 1 \cr 0 \cr 2 \cr 0 \cr } } \...
3
votes
1answer
1k views

Calculating a basis of vector space $U \cap V$

So I have two vector spaces: $ U := \langle(1,2,1,2), (1,2,3,3), (1,2,2,3)\rangle $ and $ V := \langle(2,0,2,1), (3,2,3,2), (0,4,0,1)\rangle $ I was able to calculate the base of both $U$ and $V$: $ ...
3
votes
2answers
370 views

Find Intersection Of 2 Sub-spaces

$U=span((1,1 ,0),(2 ,0 ,1))$ $W=span((1,1,1),(5,3,1))$ what is $U \cap W$? can I find the rref of them both and to find the intersections? that mean $U= \begin{pmatrix} 1 & 0 & 0.5 \\ 0 &...
2
votes
1answer
518 views

linear algebra linear transformation

I would really appreciate if someone could help me with this question, I know that you have to row reduce each matrix and put it in vector parametric form to find $U_1$ and $U_2$. any help would be ...
1
vote
1answer
210 views

Method for finding intersection between two basis

What is the general way to find a basis for the intersection of two sub spaces? There's the method that use the fact that if we take some vector $v\in V$ and $v\in U$ then every linear combination ...
2
votes
1answer
302 views

Unexpected results in vector spaces intersection

Basing on the answer to this question I tried to solve an exercise which asks to find the intersections of four vectorial subspaces. I have the subspaces $X_O=\{(1,0,0)\}$, $X_{NO}=\{(0,1,0),(0,0,1)\}$...
1
vote
3answers
108 views

How to find the set of solutions of $Ax=By$ for $A,B$ matrices?

Let $A,B$ be arbitrary matrices with the same number of rows. How can we find the set of solutions $x,y$ to the matrix equation $Ax=By$? I understand that this problem is probably related to that of ...
1
vote
1answer
171 views

Find basis and dimension of the intersection of W1 and W2.

W1:= {(x,y,z) : x,y,z E R, x+y -5z = 0} ⊆R^3 W2:= ⊆R^3 , e1 := (1,0,0) and e2:= (0,1,0) I need to give a description of the intersection of W1 and W2, and find the basis and dimension of the ...
0
votes
1answer
109 views

Finding $\dim(U\cap V)$ of two different vector subspaces in $\mathbb R^4$

$U=sp\{(1,2,1,0),(-1,1,1,1)\}$ and $V=sp\{(2,-1,0,1),(-5,6,3,0)\}$ My try is $U\cap V$ = $sp\{(-5/4,2/4,3/4,1)\}$. Then $\dim(U\cap V)$ = $1$ Do I have the solution well?. Help, please. I'm very ...
0
votes
1answer
123 views

Finding basis for intersection of vector spaces.

This method of finding a basis of two subspaces is abstracted from How to find basis for intersection of two vector spaces in $\mathbb{R}^n$ where $U$ and $W$ are the subspaces. 1) Construct the ...
-1
votes
1answer
64 views

Basis of sum of two vector spaces

Find basis of sum of two vector spaces $ V_1 + V_2 $, where $V_1$ is set of generators: \begin{split} V_1 = \space <\begin{bmatrix} 1 \\ 3 \\ 5 \\ -3 \end{bmatrix}, \begin{bmatrix} 1 \\ -1 \\ 1 \\ ...
1
vote
0answers
52 views

Find basis for intersection of span of vectors and equation

I have two subspaces $U=x_1+2x_2+x_3-3x_4+x_5=0$ and $V=\text{span}((1, 2, 0, 1, -1)^t, (-1, 0, 3, 2, 0)^t, (1, 0, 0, 0, 1)^t, (0, 2, -3, -1, -3))$ I rewrote $U$ as $ \begin{pmatrix}x_1 \\ x_2 \\...

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