# Tagged Questions

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### Prove that $b^2 pr =q^2 ac$ using matrices

Let $i_1,i_2$ and $j_1,j_2$ be non-zero real roots of $ax^2+bx+c$ and $px^2+qx+r$ respectively, where a,p $\neq$0. If the system of equations $i_1y+i_2z=0$ and $j_1y+j_2z=0$ has a non-trivial ...
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### Matrices and solving 3 variable systems

The problem is as follows: You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash ...
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### When is the equation $Ax = b$ solvable in the integers?

Let $A$ be an $m\times n$ matrix with integer entries, $b$ a column-vector with $m$ integer entries. Suppose the equation $Ax = b$ has infinitely many solutions. It is clear that the general ...
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### Solve a system of linear equations

$\newcommand{\Sp}{\phantom{0}}$There is a system of linear equations: \begin{alignat*}{4} &x - &&y - 2&&z = &&1, \\ 2&x + 3&&y - &&z =-&&2. ...
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### Method for Finding Matrix-Inverse Through Gauss-Jordan?

When trying to find the inverse of the n$\times$n matrix $A$, one way of going about it is by solving $AX=I$, wherein $I$ is the n$\times$n identity matrix, and $X$ is some n$\times$n matrix which is ...
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### Matrices in systems of linear equations

I've been working on matrices lately. Currently, I am stuck on solving systems of linear equations using matrices. I've read the following article which has proved very helpful in understanding the ...
How can I find out the eigenvectors for this matrix: $$A= \begin{pmatrix} -3 &0&0\\ 0&3&-2\\ 0&1&1 \end{pmatrix}$$ I found the eigenvalues: $\lambda_{1}=-3$, ...