# Tagged Questions

Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

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### Determine whether the system $A\mathbb x=\mathbb b$ is consistent by examing how $\mathbb b$ relates to the column vectors of $A$. [closed]

10. For each of the choices of $A$ and $\mathbb b$ that follow, determine whether the system $A\mathbb x=\mathbb b$ is consistent by examing how $\mathbb b$ relates to the column vectors of $A$. ...
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### Sizing image but need math equation

Here's my issue. I have a website mainly of images, but the image producer creates them to be too big for an average screen size so I'm looking for math equations to use to automatically size them to ...
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### Langrage Multipliers with two constraints (Efficient Calculation)

Suppose I have to minimize $x^2 + 2y^2 +3z^2$ under $x+y+z = 1$ and $x+2y+3z = k$ where $k$ is a constant and I also require $x,y,z$ to be between $0$ and $1$. I know the traditional way of Lagrange ...
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### How to find the matrix for this transformation relative to the standard basis

I'm having a lot of trouble with this problem. Any help would be appreciated.
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### Do the eigenvalues and the roots of characteristic function coincide for the matrices with entries in a P.I.D?

I encounter with a problem like this: Let $R$ be a principal ideal domain, A be an upper triangular matrix in $R^{n\times n}$, then the set of eigenvalues of A is same as the set of diagonal entries ...
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### Cross product in uneven matrices

I don't need help with dot product, only the cross product section. Even a hint as to where to start would be great.
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### On some propreties of orthogonal complements

In my book the following propositions on orthogonal complements are given without any proof. However, I cannot figure out how to prove them, even though they must follow directly from the definition ...
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### Graph connectedness algorithm idea

Assume we are given a list of edges of a graph. For instance in edge i we are given node numbers a(i) and b(i), being the starting and ending points respectively. I need to write an algorithm to ...
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### Show that the step function is linearly independent

Consider the set V consisting of all functions $f : \mathbb R \to \mathbb R$, considered as a vector space over $\mathbb R$ with the usual definitions of addition and scalar multiplication. Consider ...
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### Solve the following in vector form:

So i did a substitution to solve the system normally, and got $x=17.67$ $y=9.67$ $z=10.67$ Where I am stuck is how to represent something like this in a vector form, maybe my solution was wrong in ...
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### Name of the matrix transform $AA^*$ given A?

There are a number of places this matrix transform making its appearance: Every positive semi-definite matrix $B$ can have a decomposition $B=AA^*$ If the matrix $A$ is a lower triangular matrix ...
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### Solve the following for $D$: $ABDB^{-1} = I$

So, here's what I know, 'I' is typically: \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} But, from that I really have no idea where to go ...
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### Matrix which is not similar to it's transposed

Let $V$ be vector space over a field $\mathbb{k}$. I can prove that any matrix is similar to its matrix transpose if $\mathbb{k}$ is an infinite field, but is this still true when $\Bbb k$ is finite? ...