I'm studying math as a hobby on my own free time. So if the question seems too simple, I'd like to apologize.
I'm given the following matrix: $$ \begin{bmatrix} 46 & 5 & 58 \\ 4 & 0 & 5 \\ 6 & 5 & 8 \\ \end{bmatrix} $$
The task is to find the determinant.
The solution states that it easily can be seen that this matrix is singular and therefore the determinant is equal to $0$. Unfortunately I can't see without explicitly calculating the determinant that it is singular. How did the author of this question make this determination? How can one see from this matrix that it is singular?
A matrix is singular if two or more columns or rows have linear dependence. This means that you can write a column (or row) in terms of other columns (or rows) by multiplying any of them with a real number and adding to other columns (or rows). For this matrix
first row = 10* (second row) + third row.