Final answer:
To find the determinant of matrix A after performing the given row operations to arrive at matrix B, we need to reverse the effect of these operations. Matrix B has a determinant of 7. Since the determinant of A is calculated by dividing the determinant of B by -7, the determinant of A is -1.
Step-by-step explanation:
The student's question pertains to the determinant of a matrix after certain row operations have been performed. Beginning with matrix A and ending with matrix B as [1 6; 0 7], we trace back the row operations. The first operation is to multiply the first row (R1) by -7, and the second operation is to add the new R1 to the second row (R2), resulting in matrix B.
To find the determinant of matrix A, we consider the effect of the row operations on the determinant. The multiplication of a row by a scalar (in this case, -7) multiplies the determinant by the same scalar. The addition of a multiple of one row to another row does not change the determinant. Therefore, the determinant of A can be found by dividing the determinant of B by -7. Given the determinant of B is 1*7 - 0*6 = 7, the determinant of A is 7/-7, which equals -1.