if either of the rows or columns of any 4*4 or 3*3 determinent is zero then what are the possibilities ?

Question

can we eleminate either of the rows/columns and then how the determinent is reduced by rows and columns.and how the following determinent
1:---wwe make a row or a column or a row zero by subtraction or adition of columns, then is it for the simplificatiooon and elemination of such rows and columns that are now zero .
2:---if only one element of the row/column is not zero then can we eleminate it?

Answer 1

if one of the columns or rows of a matrix is zero, then the determinant is equal to 0. .

Answer 2

If any row or column of a determinant is zero, the determinant will be zero.

If any one element of a row or column is not zero, it can't be eliminated...but it makes computing the determinant much easier if you use that row, because you'd only have to compute one "minor", if you're familiar with that term.

A row of all zeros means that you're missing an equation; that is, that you have 2 equations with 3 unknowns or 3 equations with 4 unknowns. This usually means the system is "underdetermined" (an infinite number of solutions).

A column of zeros means that you're missing a variable; that is, that you have 3 equations with 2 unknowns or 4 equations with 3 unknowns. This usually means that the system is "overdetermined" (no solutions).

The only way I could imagine that it could still work with a row or column of zeros would be something like this:

| 0 1 2 | .| 5 |
| 0 3 4 |=| 6 |
| 0 0 0 | .| 0 |

In this circumstance, it's not really a 3x3 system; it's a 2x2.