$M=(a_{ij})$, with $1\leq x\leq3$ and $1\leq x \leq 3$, such that $a_{ij}=4i+2j-6$.

Question

My exercise asks me to write the following matrix $M=(a_{ij})$, with $1\leq x\leq3$ and $1\leq x \leq 3$, such that $a_{ij}=4i+2j-6$.

What I did not understand, and tried unsuccessfully was what is this

$1\leq x\leq3$ and $1\leq x \leq 3$

It has something to do with the order of the matrix? Or something?

Answer 1

My guess is that there is a misprint or transcription error, and it should read $1 \leq i \leq 3, 1 \leq j \leq 3$.

Answer 2

Since the variable $x$ is referenced in neither the expression for $M$, $M = (a_{ij})$, nor in the defining equation for the a $a_{ij}$, $a_{ij} = 4i + 2j - 6$, it strikes me that the ocurrances of $1 \le x \le 3$ are misprints for $1 \le i \le 3$ and $1 \le j \le 3$; under this assumption, the whole thing makes sense, and we have for example $a_{23} = 4(2) + 2(3) - 6 = 8$ etc. Defining matrix entries in terms of their indices is a common practice and so I strongly suspect that is the intent in the present case.

Hope this helps. Cheers,

and as always,

Fiat Lux!!!