AA and BB are n×nn×n matrices. Check the true statements below: A. If two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix. B. The determinant of AA is the product of the diagonal entries in AA. C. detAT=(−1)detAdetAT=(−1)detA. D. If detAdetA is zero, then two rows or two columns are the same, or a row or a column is zero.

If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix. ( A )

Step-by-step explanation:

A and B been n*n matrices the true statement would be ;  If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix.

Although other options can be true for some matrices but they are not always true for every kind matrices but option A is always true

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

answer: -10

step-by-step explanation:

s(t) = 1 - 10t

s(x) = 1 - 10x

s(x + h) = 1 - 10(x + h)

            = 1 - 10x - 10h

s(x + h) - s(x) = 1 - 10x - 10h - (1 - 10x)

                      = 1 - 10x - 10h - 1 + 10x

                      = -10h

= -10