Question

find the value of bye expanding along a)2nd row b)third column interpret the result​

Answer 1

Finding the determinant of a 2×2 matrix is easy: You just do the criss-cross multiplication, and subtract:

determinant of a 2-by-2 matrix

The process for 3×3 matrices, while a bit messier, is still pretty straightforward: You add repeats of the first and second columns to the end of the determinant, multiply along all the diagonals, and add and subtract according to the rule:

determinant of a 3-by-3 matrix

But for 4×4's and bigger determinants, you have to drop back down to the smaller 2×2 and 3×3 determinants by using things called "minors" and "cofactors".

A "minor" is the determinant of the square matrix formed by deleting one row and one column from some larger square matrix. Since there are lots of rows and columns in the original matrix, you can make lots of minors from it. These minors are labelled according to the row and column you deleted. So if you were to go, say, to the a2,4 entry from some matrix A and cross out the row and column that pass through that entry (that is, if you remove the second row and the fourth column of the matrix), the determinant of the new (and smaller) matrix is called "the minor M2,4"