In other words What is the determinant of det A which equals

In other words:

What is the determinant of det A (which equals 5) if v1, v2, v3, and v4 are rows in a 4x4 matrix and v1 or row one

is unchanged, row 2 is now 4v2 + 5v4 (or 4 times row2 plus 5 times row4),

v3 or row 3 is unchanged, and row 4 is now 3v2 + 6 v4 ( or 3 times row 2 plus 6 times row 4).

then det

v1 4v2+5v4 v3 3v2+6v4

=

Solution

On multiplying the row by a constant factor, the determinant will become k times the original determinant

The first row has not been altered, hence it will not affect the value of the determinant

The second row has multiplied by a constant factor 4, hence det(change) = det(old) * 4 = 5 * 4 = 20

The third row has not been altered, hence it will not affect the value of the determinant

The fourth row has multiplied by a constant factor 6, hence det(change) = det(old) * 6 = 20 * 6 = 120

Hence the determinant of the given 4X4 matrix will be equal to 120