How to calculate Ax=7x for matrix A (3x3)

Question

How to solve this equation for 3x3 matrix A? Ax=7x

I already know the matrix A and need to solve for all solutions x

Answer 1

Short Answer:

$Ax = 7Ix$, where $I$ is the identity matrix $3 \times 3$.

Then this is $(A - 7I)x = 0$. Use Gauss-Jordan elimination.

For Interested Persons:

In this example, 7 would be called an eigenvalue. An eigenvalue is when you multiply a matrix by a certain vector(called an eigenvector), that vector gets scaled, and the amount by which is scaled is the eigenvalue. For example, when you do $Ax$, the product is scaled by a factor of 7 to get $7x$

Here, we use I so we are subtracting a matrix from a matrix, not a scalar from a matrix.