Question

Give an example of a$\mathbf{3}\mathbf{\times }\mathbf{3}$ matrix with all nonzero entries such that $\mathit{d}\mathit{e}\mathit{t}\mathit{A}\mathbf{=}\mathbf{13}$.

Short answer

Therefore, the example of $3\times 3$matrix is given by,

$A=\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& 13\\ 2& 1& 3\end{array}\right]$

Step-by-step solution

Matrix Definition

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be a “ m by n” matrix, written “ $m\times n$.”

To find  3×3 matrix

We want to find amatrix,

$A=\left[\begin{array}{lll}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$ , with all non-zero entries, such that:

$aei+bfg+cdh-ceg-bdi-afh=13$

For $a=b=c=1$, we have

$ei+fg+dh-eg-di-fh=13$

For$f=13,g=2,h=1$ , we're left with:

.$ei+d-2e-di=0$

For$d=1,e=2,i=3$, the equation applies.

So one example of such a matrix is$A=\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& 13\\ 2& 1& 3\end{array}\right]$