# Tag Info

1 vote

### What is this condition?

In order to have a vector $c$ with $Ac=b$, you need $b$ to be in the column space of $A$ (since an expression of the form $Ac$ is a linear combination of the columns of $A$.)
Accepted

### $\frac{x^2}{x} =x$ isn't an equation true for all values of x?

Yes, many mathematical statements (such as equations) are only true under certain conditions (such as restrictions on the values of variables). It's common to express these as if-then statements, as ...

### $\frac{x^2}{x} =x$ isn't an equation true for all values of x?

In this case, the equation $\frac{x^2} x = x$ should be thought of as a condition, selecting for particular values of $x$. In particular, this equation is equivalent to the condition $x \neq 0$. Your ...

### Solve simultaneous equations

Rewrite the last equation as $$\lambda_g-\lambda_d= k \big[\lambda_d\big]^{-2/3}$$ Cubing both sides gives a pentic equation in $\big[\lambda_d\big]^{1/3}$ : so, no explicit solution and a numerical ...
Accepted

Accepted

### System of inequations

Rewrite the inequalities like this: $$q+r<s+t<p+q<r+s<t+p$$ From this, we immediately see: $$\begin{array}{c}q<t\\r<p\\q<s\\t<r\\s<p\end{array}$$ (Say, concentrate on the ...
Accepted

### Cramer's rule and centre of a circle

To be more pedagogical, he should have had the last row be all $1$'s so as to match the variable he states i.e. $R^2 - |z|^2$ as you say, but the end result is the same - by determinant rules, you can ...
1 vote
Accepted

### How to solve for m in this equation without using the quadratic formula

Converting a comment to an answer, as requested ... If all you know is that $m_1m_2=2$ (where $m_1$ and $m_2$ are the roots of the quadratic), then you can't find a specific value for $b^2−a^2$. By ...
The blue line $y=2-x$ cuts the parabola $y=x^2+2x+2$ at $(3,-5)$ and $(0,2)$. But when you put y=5 in the second equation, you are actually solving the parabola with the green line $y=5$, which cuts ...