# Linked Questions

1answer
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### 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 ...
1answer
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### 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 ...
2answers
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2answers
370 views

$U=span((1,1 ,0),(2 ,0 ,1))$ $W=span((1,1,1),(5,3,1))$ what is $U \cap W$? can I find the rref of them both and to find the intersections? that mean $U= \begin{pmatrix} 1 & 0 & 0.5 \\ 0 &... 1answer 518 views ### linear algebra linear transformation I would really appreciate if someone could help me with this question, I know that you have to row reduce each matrix and put it in vector parametric form to find$U_1$and$U_2$. any help would be ... 1answer 210 views ### Method for finding intersection between two basis What is the general way to find a basis for the intersection of two sub spaces? There's the method that use the fact that if we take some vector$v\in V$and$v\in U$then every linear combination ... 1answer 302 views ### Unexpected results in vector spaces intersection Basing on the answer to this question I tried to solve an exercise which asks to find the intersections of four vectorial subspaces. I have the subspaces$X_O=\{(1,0,0)\}$,$X_{NO}=\{(0,1,0),(0,0,1)\}$... 3answers 108 views ### How to find the set of solutions of$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$? I understand that this problem is probably related to that of ... 1answer 171 views ### Find basis and dimension of the intersection of W1 and W2. W1:= {(x,y,z) : x,y,z E R, x+y -5z = 0} ⊆R^3 W2:= ⊆R^3 , e1 := (1,0,0) and e2:= (0,1,0) I need to give a description of the intersection of W1 and W2, and find the basis and dimension of the ... 1answer 109 views ### Finding$\dim(U\cap V)$of two different vector subspaces in$\mathbb R^4U=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 ... 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 ... 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$is set of generators: \begin{split} V_1 = \space <\begin{bmatrix} 1 \\ 3 \\ 5 \\ -3 \end{bmatrix}, \begin{bmatrix} 1 \\ -1 \\ 1 \\ ... 0answers 52 views ### Find basis for intersection of span of vectors and equation I have two subspaces$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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