# Tagged Questions

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### shortest point on a line segment from point out side the line

from the above pic I found the value x from line (p1,p2) and point a using y=mx+b and imaginary red line which is perpendicular to black line having slope -1/m and the intersecting point x. the ...
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### Decompose a real symmetric matrix

Prove that, without using induction, A real symmetric matrix $A$ can be decomposed as $A = Q^T \Lambda Q$, where $Q$ is an orthogonal matrix and $\Lambda$ is a diagonal matrix with eigenvalues of $A$ ...
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### Linear Maps from a finite space to an infinite space

Suppose V is finite dimensional with dim V > 0. Prove that if W is infinite dimensional then $L(V, W)$ is infinite dimensional. Help? I really have no idea how to go about this one? I'm assuming I ...
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### Determine whether or not a set is linearly independent

Prove or give a counter example: if $v_1, ..., v_n$ is linearly independent, is $5v_1-4v_2, v_2,...v_m$ also linearly independent. I'm not sure how to go about this. I tried a couple ways to prove ...
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### Finding a basis for a set of polynomials

Let $U = \{p \in P_4(\mathbb{R}): p''(6) = 0\}$. Find a basis for $U$, then expand that basis to be a basis of $P_4(\mathbb{R})$. So I've been trying to find examples on how to approach this. I am ...
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### Let $T : M_{\text{2x2}} (\mathbb{R}) \rightarrow \mathbb{P}_2$ be a linear transformation give by … [closed]

Hey guys could someone who is good at this take a look and tell me if I did it right =) I did all the work so it shouldn't take long to verify my results ... Thank you in advance Problem: Let ...
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### In each part, find a basis for the given subspace ofR 3 , and state its dimension

guys I gotta be honest, I've taken notes on everything in the last two sections for this but I'm not sure how to find a basis for a subspace that is a lone plane/line etc.. a full explanation would ...
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### Seeking Help on Linear Algebra Problem, Thank you all (YES or NO ANSWER)

Did i do the 1st one correct? Having difficulty understanding 2...1 step at a time just want to know if i did 1 correct
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### the volume of pyramid value

when calculating the volume of pyramid using a determinnat, is it ok to take the determinanat in absloute value so that every negative result would be converted to positive volume number?
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### Calculation of eigenvalues in a Markov Chain

I'm trying to solve this exercise: Finding the eigenvalues of $A=(p_{ij})$ where $\sum_{i=1}^3 p_{ij}=1$ for all $j=1,2,3.$ In the $2 \times 2$ case have $\lambda_1=p_{11}+p_{22}-1$ and ...
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### $SO(n)$ is connected, alternative form

I have the following exercise: Show that $SO(n)$ is connected, using the following outline: For the case $n = 1$, there is nothing to show, since a $1\times 1$ matrix with determinant one must be ...
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### Vector calculation question

the points a b c d are concordantly ( 1,2,-3) , (-1,2,1) , ( 0,1,-2) , ( 2,-1,1) find formula of the plane going thorugh d and which is pararlel to plane abc calculate the volume of pyramid abcd. ...
Thank you ahead of time for the help, I am having a problem with part $4$. I understand parts $1$ and $2$ and $3$ and have solved them but I cant seem to understand $4$. If someone could help me out, ...