Final answer:
The question is asking to calculate the determinant of a matrix by expanding along the first row and second column. The process involves multiplication of each element in the chosen row or column by the determinant of the submatrix remaining after omitting the element's row and column, considering the alternating signs.
Step-by-step explanation:
The question requires finding the determinant of a matrix by expanding along the first row and second column. This process involves taking each element in the chosen row or column, multiplying it by the determinant of the submatrix that remains after removing the row and column that the element is in, and considering the sign associated with the position of the element. The signs alternate starting with a positive sign for the top-left element of the matrix.
First, you select the element from the first row, second column. Let us assume the element is a. Then, cross out the first row and the second column which leaves you with a smaller matrix. Calculate the determinant of this smaller matrix. Multiply this determinant by a and consider the sign (+ or -) based on the element's position, which is given by (-1)i+j, where i and j are the row and column indices of the element, respectively.
Continue this process for each element of the first row or second column, depending on the chosen expansion. Sum the results to get the final determinant value.